{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 3) (100,)\n"
     ]
    }
   ],
   "source": [
    "X, y = make_regression(n_samples=100, n_features=3)\n",
    "print(X.shape, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 1)\n"
     ]
    }
   ],
   "source": [
    "y = y.reshape((-1, 1))\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1605221f508>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9, 4))\n",
    "plt.plot(y, alpha=0.5, linewidth=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x160522ab4c8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(range(1, 101), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_sk = model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x160523b0e88>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9, 4))\n",
    "plt.plot(y, color='green', linewidth=4)\n",
    "plt.plot(y_pred_sk, color='red', linewidth=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gd(X, y, theta, l_rate, iterations):\n",
    "    cost_history = [0] * iterations # 构建一个包含iterations个0的列表\n",
    "    m = X.shape[0] #将样本数据的行数取出， 赋给m\n",
    "    for epoch in range(iterations):\n",
    "        y_hat = X.dot(theta) # 针对线性回归\n",
    "        loss = y_hat - y # 计算损失函数\n",
    "        gradient = X.T.dot(loss) / m # 为什么？\n",
    "        theta = theta - l_rate * gradient # 根据梯度对参数进行更新\n",
    "        cost = np.dot(loss.T, loss) # 计算均分误差损失函数值\n",
    "        cost_history[epoch] = cost[0, 0]\n",
    "    return theta, cost_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 训练：随机取一个起始样本（ 起始点）\n",
    "theta = np.random.rand(X.shape[1], 1)\n",
    "iterations = 100 # 设置迭代次数\n",
    "l_rate = 0.1 # 设置学习率\n",
    "# 采用自建的梯度下降函数进行训练\n",
    "theta, cost_history = gd(X, y, theta, l_rate, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[49.04414677, 74.19927044, 94.61907401]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[49.04322548, 74.20224438, 94.62227394]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x16054405208>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(range(iterations), cost_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(X, theta):\n",
    "    return np.dot(X, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x160544a0788>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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haS/s6903kYdpkAN9oT7K4sqoGvQWSTGJKMVkNpVy6qwcGP33Go9JcaC9aIUSk3gizlB0KNVjMomlnLnBpL8EZqb5dc6QFblvqUEz+TM+XTFuYiKlPCal3GR9PQDsAFqBq4CfWnf7KfAm6+urgJ9JhWeAOiFEy3iPo1BUeavsExNZeClna7NSTI4OHB1TZobB+BAIqTh6XcMvhmISjAbVIuwgJuF4mHCssO6e6QInMRnwKiVwKhCTx/Y9xqt++CquuusqDgUO5f17CZlgd/fuKZHkmeIxIX9ioglAVQSGy5Ri0h/uR0o50YeckvpqH88MU0y6h7qZM6QmJ8+Gzcd0RVE9JkKIJcB64FmgWUp5zPrRcaDZ+roVaHP82mHrtvTHulkIsVEIsbGzs7OYhwkoYhJ3q/He5dHCSzlb5inFBOBg38GiH5/ByAiEA9SGk6mvxTK/pismMDUu1hMBPZ25z688EFNhkQ7Hwlxz7zX0bn6aJ198kH959F/y+r2ETHD5nZez8lsrWfHNFXm3/08UNDEZ8KrvBy3iN9o6Y68xEThSrRSTuIxPimLREeygaShpfIWkYjIcG54RM2W0YmKIydRG0YiJEKIK+DXwUSllyjstFd0viPJLKe+QUm6QUm5oamoq1mHaqPZWA4XVfrMpJmB8JqWAPcBPE5NiKCaRYIbHBGbuwpVeyqmOlN78urd3L72hXj7zZ7jqFXjm8DN5/d7fDv2NR/Y+wv/3Z6Cjk288+42JPMxR0R/upzqSVEwGvPmZX/U6VBVRPog66xSeDBVIx9GnlHIcE4Z1AOF0hiEm0wNFISZCCA+KlNwppbzfurldl2is/zus248ACx2/vsC6bVJR5a0CCiMmTo/JlmZYZikmpmV48hEIBWzjKxS3XTjomfnEJBwLMxwbTinlTIVF2jmvqCacP1HSm4Mbt8Cp7bCze+eEHWM+GIiMzWNirzFWlH2tJiYT3Jkjpcwo5WgfXqU13Hi6d+aEY2EGIgM2MQnMgqyi6YpidOUI4IfADinlVx0/ehC40fr6RuABx+3vsrpzzgYCjpLPpEETk3x3MpA6MXTnHKgfBn/UKCalwIQoJtFM8yvMzIVLX+hSFJMp4DHRxKQimrxo5OOv6B7qBqBxCFr74Uj/pO91bMQSMYaiQ1mJSTASHLEkkq6Y6Nj0iVZM+kJ9xBIxO8OkylvFnIo5SR8e099n0j2szhGjmEx9FEMxORd4J3CREOJF69/lwP8ArxVC7AYusb4H+AOwD9gDfB/4xyIcQ8FwKib5Bh8NhAdwx1Xk+aAXDtXCkj7TmVMKTIRiMptKOc44+qnkMUknJnEZZzg2POrv9Qz34I5DXRhaB+DY4LGSeSK0yuPMMdHrjEQyHM399zg9Jm2TqJikp742VTRR6alMKeVM984cZ+qrISZTG2XjfQAp5VOAyPHji7PcXwK3jvd5x4v0Uk5/nqWc6ohlaBOwv14ZYI1iMvnIqpi4x05MEjLBcGx41igm6cRkqnhM0okJqNe/wlMxwm8pYqL9GK39SrXoCHYwr2reRB5uVjiVVdtj4kt60gYiA1R6K7P+rt4g2aUc6zWY6CwTnfqqB/jNrZyLRNrmV5j+iomTmHSXG2IylTF7k199YzO/OuXZ/XVWyJrxmEwqpJT0h/uLqpjoXexs8ZhkKCaWxyQYDRY8lbmYyEVMRkNPqIcGS4hotbhVqco5uhyWrZQDI681+nftUs4kmV/1ZGE9wK+pcvYoJgORgRnRcTSTMGuJyVjNr9UOeVYrJr2h3imRnTBbMBgZJCETtmJSXlaOx+3BX+YnPEZi4jRdzqZSjm651h4TKK3JcczEZFgRk4hLKSYARwZKQ0yc3XsFE5Ms7cJQmlKOznqaiYqJk5jA9Df2zjTMemKiY+nHopjsq3d05phyzqTBeVEN+NRkYQB/mZ+IGzxxEInCiIneDepSTtCrCI47PrOJSbrHBEr7946XmLwyp/SKyXiIyWBkEJFQf397lUo2LotPvGLSEewAid2VM7dyLpXemaeYiAQ0DEN3xczffExnzHpioheMfGrrA2GHx4RkKQdMOWcyYc/J0QP8/LWAIiYICJcpg3JBxMTaDepSDsJKQ52hkdXZSjl6cFwpO3PGQ0wah2FHk+rMKYuXXjFxrhU6YA1GL+VURCFUBgmXunjWhiZBMQl2UhtSzxv2JM2vM6lduGuoi9qw+nzH3MnXFmbmZ3w6Y9YSk/KyclzCZS8Y4XiYaDw64u/kKuWA6cyZTOjdo76o1vocxARsn8lYSjlaMYGRzXEJmSipF2O86Av14YmBN540+06FCcND0SHK4uAtcPpr91A3DcPKuNlZCfMGS0dMnF056QFrzp9ngx7gN2gRmoB/ciYMdw51pqS+2h6TGdQu7AxXg1TFxJTipxZmLTERQmQM8htNqkwv5fSUg0tC3bAp5Uwmsk0WhvERE/3ea48J5CYm29q3sfy25ZR9rox/e/zfxvvnZCAUC9m5HBOFvlBf0jwsplYpp9zaH+R7PLFEjEA4oCT6cuXNKGWWybg8JpFUVbbPbykmk1DKcaa+ZpRy5Mwo5eQiJkYxmVqYtcQEMicM5zPHwrlomJbh0kAv0nYpp4iKiV3KITcx+fxfP89Q236u3Qb//dR/F7WMt71jOyu/uZI5X57DDfffMGHD25xx9JBsF4bSl3IqotCnLxpy9IuGLks1DKvNwpEamD9Q4lKOtErEY/CYpCgmvklUTBypr7qUE3NDQihlbSYrJoaYTC3MemIykOeCIaXMiJkG0zI8Xmw8upFH9z5aULtehmJSBGKiF918SjnbO7bzqjb4yLPq+2LGn//v0//L0LE2Pvgs3LntTl449kLRHtuJdGKi24Wh9IpJRRR6y0EKZf4c7Xh6hnuAJDE5Wq0MsKVUTCojSZ+IW7gL6spxlosDlmIyGTkmzlKOVkzAMWF4BigmjbOAmAQjQfb07JnWpeZZT0wG86z9DkWHSMiEvWgIK1NOd+Yc6DswKaPJZxK+8vevcMb3z+B1v3gd1//6+rx/L0MxmaBSTq5ZGu3BdpqD2LkZ+sJYDLzc+TKnH4MPadLTNTEzX7IqJlPEY5IeclcoMdGlnEA4UJJdfvoGpqW6hXAZlCWUKXdMiskElnKklHQNdaWUcpoqm+wGAd0ybBSTqY/d3btZfftqVnxzBRf+9MJRfZNTFYaYOLoR8gk+0qPM51TMocZXY5dyhmPDtAfbJ+OwZwT29Ozh3x7/N67ZDv/yFNzz0j0c7j+c1+8GwgHK4uBJqAvYZJpfY4kY3UPdzA2q7g+gqH6QowNHmT+ggq4gmS9RbGQoJlNkkdbEJDgGYtI4lCzl2C3DJSjnpHvRWqpabB/PaHO50j0mWjGZyFKOnpOjU1+rvFX4y/xUelIVk8Ho9O3KGYoOMRwbTiEmdidaHuXC6YJvP/9t+joP81+Pw1OHnuJ3u35X6kMaEwwxyVNidbYA9vugxlfD0rqlKS3DpjMnf/zrY/+KbzjKbQ/BG3ar23Z07sjrdwMhFUffbxk3i6KYpLcLk/3C2DXUhUTSPAj1IZWXUizFJCETHBs4xvwBNfPFE0tGhRcb6cQkUqZKJ97Y1PCYFEMxgdKUc9KJyfzq+UB+YY65FJN8hxmOBXYc/VAywwSwSzm6ZXg6KyZ68+AkJnG3WisqZ1AkwMtdL7OmEz7+NCCVApsN29q38Zk/f4Y/7v3j5B5gnpjVxKTaW114IqNVyqn2VbO0fmlKy7DxmeSHJw8+yf077udfn4Jtc2GlJTjs6t6V1+8HwpkD/GD8iolIQHkUhtOIiTOmXS/ic4PglurnxSImncFO4jLOfIsXNA1NHDEJhAMpxASSPpOpoJgUQkz0RUcHZ00FxcSpehRCTLJ5TOpCirROVI6IVuV0KaepogkgqZhYLcPT2WOSnvqqMdPm5bQF2lgYgPKYej8P9B3IuM/h/sNs+P4GPven/+T1v3g9D+1+aPIPdBTMamJS5a2y5VXITzHRO6FqbzXL6pZxoA4WB9TO2XTmjI6ETPDxRz7Owj74wEb4h6vUa1odyp+Y9IX6Mgb4wfg9Jv6YCmdLWJ8KZw1aqwiaKDRba3TDsJrTUgwcHTgKYBOTucGJISaReISh6FAmMbF8JtNRMXFZuSd9fodiIpOv6WQi3WPSWt0KJEPWcq0zUkoGI4NZ24Vh4so56QP8miotYpJufp3GismoxCQy/YmJlJK2/jYWWn/Kkj44EDiQcb/f7PgNkXiEXd+EpkG4f8f9WR/rD7v/wMajGzncf5hIPDKxB5+GcU8Xns4opJSjF2u9aMzz1bC0filD1lyVeYNGMckHd25VnSY/fxxuPwPa6mB3A6zogV0941NMfGXqhrGWcpxlHMg0x9X562gfVD6iuUEY9FjEpEiKiZOYDHgnjpg4A+qOzUnePhV2j05iEi7LL3m3Z7iH2pAiVgkXDPhVWaomPDVKOS3VLcDoikkoFiIu41RFoNcijLqUA+p9W1CzoOjHmz7A77QKq5TjUEwqo3Bwhigm3RVQ4algKDo0Jc75YqEv1MdgZJBFFn9d3Acv9h3MuN/e3r1UheGEXqUsHg8ez/pYb/jlG+zvq7xVDHxq8jYss14xsZMN5SimNEeao13KqVsKJDtzjGIyMoaiQ3zq8U9xxmF4zQH40rnq9l2NsKK7gFKO5THpK6JiMhQbSjG+QnbXvq2YDKq5LI3DxTO/OonJlmZrbskEmF/T4+g1tBlw2nXlWJOFe8qTt9kha1PA/KpLOTqaINc6Y29+srQLw8QpJp1DnSDVRbtzligmy+qXAVODjBcLbf1tACwMQFuNUkwOBg5mRDHs691n2w9ybX50I8fH/w5nHk76jiYLs56YxN0QcStvQV7mV2vBqfEqxQQcWSaGmIyIrz79VY70H+Grj8D/9xqIVii9elej8pkc6DuQl2RoKyaamBQpx8TZKgzZiUl7sB1vTHXv7G0ormJybPAYIqFIz9bmiVNM0omJbn13joEvFcZayskgJpbPZLKJiZRSeUwc5CJfj4m+PZv5FSYuy6Qj2EFtSHmrImXJi1BGu/A0UUyCkWDGZ79rqAtXQp3zvf4ZSkwCFjHph78uUsQkEo/YKq/Gvt59nDAaMbF+5w271DWvubJ5Qo89HbOamFR7q4E8TWlppZxqXzVL6pYAyfTXQ4FD07ZvfKJxfPA4//PU//DWl9Vr/dN18JGzPsKCmgU2MUnIRF6dTYGQMm7apZxiKCbRISrzVEy0SbC7vPilnDlDinAdrrHKRZFBu5W5WEgnJvOq5gFJj0mpFmkpZVZiEo6HCcfCOX9PD/DLqphMciknFAsRS8RsxcTr9tJY3giMvs7YBvss7cIwcVkmnUOddhkHsphfdbvwNBji9+nHP03Vf1ex5OtL+Hvb3+3bu4a6qB9Wr2fcDcvqFDEJzCBicihwCFCKyV8XK+8jpBpgpZTs693HslGIyfFBVd5pDqop181V05CYCCF+JIToEEJsd9zWIIR4VAix2/q/3rpdCCFuE0LsEUJsFUKcVoxjGAvSJwyPppi44+qCF/QqUlPhqaC5stlWTBIyYctpBqm47+X7CEaC/M9j8E+vh/rKRv7t1f/GysaVNjGB0cs5CZmgP9yfan7NoZiE46kXs+6hbr7+zNe5f8f9Ga2XwWjQzs8AqPfX51RM5gahvVJdCBuGoTfUW1BybS7oDJOj1cqEaGeZBDPLOQPhAR7b95gtURcCTUx0OWxR7SIgGUufXsp5pesVzvj+Gcz/3/l8/4XvF/x8+SKaiBKX8QxiAiOrOFox6c6imBwbPFaU9yZfOPOOtEm+2pfcAFWPQzGZSPNr+gA/gHJPuX3clVHLAzOF00SPDRzjv5/6b67bBpVt7Xz6iU/bP+saTg1Xm5GKSX8bnpgqVz29QCkmkEpM2oPtDMeGWdaryHvzoNqUpZfpdCmneVCtddNVMfkJcGnabZ8EHpdSrgAet74HuAxYYf27GfhOkY6hYGhiMpCPYhIeSC4YQuWYAKZlOE8cChzCH4MF/fDEMrhlwy3U+etY2bCS3ZqYyNGJyY7OHUgkC/rVDq/KW4XHrdiEz51qfo3EI/ZFKZ6Ic/YPz+Zjj3yMt97zVr7+zNdTHje9lNNS3ZJTMWkeVIt4d4UiJgmZKMpuNp2YNFlCSbrPpDPYyfJvLue1P38tp3znlILzc9IVk4W1C4Hc7cKffuLTHNq1kVXbjvHBhz7IsYFjY/sDR0F6yF2+yZx6srBWTNzCbSsmsURswlqusyG9e6/GV2MrD3oDFIwEs5KlUT0mE6WYBK05OY44egCXcFHhqUiZMFxs9a6Y2Nu7F4nkHzbDlTvh2cPP2kQqPfU1GzGZ7sndbf1tioxXK9/jkj5AKp+Jhl4rlvXCMwuSm5/0z0j7YDtlcUWKuyuSqupkoSjEREr5JJCuZ18F/NT6+qfAmxy3/0wqPAPUCSFainEchSJdMRlpV9YfSTW06V3QsvplKSFrxmeSHekqR0uVestXNq6kpwLiLmX2HI2Y3PPSPbgSauH5wwp41cJX2T8TQuBz+2xiAtglgM3HN7OnZw+/vA9efQDufunulMd1lhBAfRCzKiaDlmJSpS6EOv21GOWcXIpJ+qLxsy0/o2Owg/+7E4a6jhc84dhJTAJ+WFCtOj10LL0ztwVg07FNvH4PfOWPiuz99dBfx/5HjoCxEJN4Ik5fqC+FmCxvWJ6aZVJgOScaj3L7c7fz2b98tmBS4wxiHPAqYuJ2uSkvK7ejCSQy6wU+m2Iy5FED9DyxiTW/ZivlgCrn2BOGmdo+k95htTusH4b1x1Qat15P0olJS3UL5WXl9jmWkIkpTbrywaHAIdv4OuCHsFutT07FJG9iEmynKahUyIRr+iom2dAspdRbq+OA/staAWe947B1WwqEEDcLITYKITZ2dk5MLLeTmIwksULmZGFbMalbSlutahf2xIxikgsZLb6WL2Rl40ogaYAdiZhIKbnn5Xs4/6CS6vc2wrUnXZtyH3+ZP4WYaJ+J/uAt61W113QVIhhNbRduqWqxCatIJHdUHcEOmq28B13KgfETk1giRnuwPS9isqdnD3OG4I274f0b4d6X72Vvz968n6sv1EeZVZYc9EJDeYOd6aOJgP4sSCk5Pnic5iCsbQd/FJ478ty4/tZcGAsxCYQDSKRNTGp8NSyuW5ya/lqgAfZfHv0XPviHD/KfT/wHp33vtLxHJTiP06mYQH7RBNk8Jggry2SC5uVIKe1SmL5oz6lI9pBXeitt8ytM7c6c3pBFTEKw3uqA3Xx8M5BJTPRIkX5HqWy6l3PaAm0sCkCbWlo5UJfszNHY17sPV0K1Ej/bmlxj0sep6Hlg7eoSOT09JqNBKo2sIJ1MSnmHlHKDlHJDU1PT6L8wBjhrv/mYX2scEqs2zi6tW0rMrS4miwKwr8/E0mdDIBRIUZy0L8RJTFb0jExMtnds55WuV7jmJbjnJChzlfGm1W9KuU8uYuLcTdVnMawORYeojKQqJgmX+r4yqhat/nA/4Xg4w2MC4ycmHcEOEjJhE5POEYjJ4YHDLOiHHj989BnwRBL879P/m/dzpQTUWZH+1d7q5OwQkuphf7ifUCykiHdC7USnEjFJj6NvLG+ktbqVIzXJoLpCFZN7XrqH67bD5u/CQOcR3vjLN+bdQu2MFej3JdeYfIhJumKi15iJnJczFB0iEo/Yr5+/zG97S/RxTxXFJJaI8XLnyznXaednfHUX+KKw+dhme0hhLmIyFWZEjRcJmeBw/2EW9sMhi5gcrFObsHTFZP6AKs8crBu5lKP9JTCzFJN2XaKx/td/+RFgoeN+C6zbJh2Fml+rHRdWvRM6oeEEQIWErerOPZtgtiMQDmRNa11StwS3cNuKybHBYzkvAve8dA/uOLz1Zbh3Dbx22WtpKG9IuU9OYmLtphqG1b++UF9KuSIYscyv2mNilZqcNWhnhkmxFRNnhsnRanVOuiRURDLNr4f7D9PaD08vhBfnwTu3wo9f/HHeZYe+cOqcnDp/Xc5FWu+k5g2qNsszj8ALx14gloiN6+/NhvEQEz3Ar6G8gdbqVtorlQnQHS9MMQlGghwbPMYp7WrRvvceeOnoFq779XV5/c25FJNqX7Wd/Ao5FJM0j4kOU7MnDE8AMUkndvX++pSfV3pSFZNSdeaEYiHO/P6ZnPTtk1hz+5qsCmFfqA9hJQDvbISTO+DF9hcZjAwSiUdsYlJeVk6Fp2JGEZP2wXaiiahdygGHYtJ30PbP6I6cffXWXKQgILOXcuYNwvEZqJg8CNxofX0j8IDj9ndZ3TlnAwFHyWdSYZtffXnOsHBIrHontLZ5LaAuEOuOK2IyUmvjTEBfqI87t97Ji8dfzPt3+sP9KaUcvWB73B6W1S9L6czZ07Mn4/d1GeeCg4rp72+Aa066JuN+IyomUvkq6tMCq3SbqrOUo81eTmKiL9LaY9LtICbdw+MLWUsnJgjLABuEjqE0xaRfKSZHquGL58G//A0ikRC3PXtbXs+VPsCvzl9Hta/abheG5M5ftw3OG1SenjOPKAIxEQS8GIpJQ3kDrTWtxN1KdZo3WBgx0TX45T3wL6+DmAtu/z38Ydcf+OjDHx3VIOnMOxqw8o4gUzHJRr4HI4N4YiBQ2UqtNarCrRWTicgxcb5+vdbr50SlN81jUqJSzr0v3cvm45v56sPQ2d3Gjzb/KOM+vaFeNdvKCy/MV+vx5mObM8LVdKlqJhET3Q3qLOUcrFXEZDg2bJeuncRk2AtRtzpXncRESqkUE2cpZzoqJkKIXwFPA6uEEIeFEDcB/wO8VgixG7jE+h7gD8A+YA/wfeAfi3EMY0GG+XUEuTY9zVHLrA3lDSyqXWQTk1gixkudL034sZcKQ9EhTv3uqdzwmxvYcMcGHt7zcF6/lzIRmGQpB8irZXhr+1Z2de/i2u2qjONxebhq1VUZ98tFTHqGe6gOQ5nMVDlCsRASaV8QfW4f9eVq55hVMbE8Jr3lFsmRxVdMIOkzcS4aoViIrqEuFvSrrJMnF6sL8ptegdufvz2vkkM2YpJrkXYSkwdXKWICE1POGS8x6a5IKiagXsfWgcJKOZoUL+9Ru+5rr4azjsA//129vqORv5E8JgOjlHJSNj8ii2IyAR6TbMTOiUpPpd0uDKUr5bx4/EXKI/CxZ1RnX7Ymg95Qr31eb56nfCbdw91sad8CJIlJY4XKlZlRxMQRrnbI4TFZ3Gd93XeAUCzEkYEjNjGB7GtMIBwgHA/bpZzysnL7WjlZKFZXzvVSyhYppUdKuUBK+UMpZbeU8mIp5Qop5SVSyh7rvlJKeauU8gQp5SlSyo3FOIaxoLysHJdw2RJrOB7OGZA2EEmd+qkXHIB189axuUXV34GClITphgdeeYBDgUM88Eto6Yvz860/z+v3AmHlMUkv5YAiJnsa4IQeZTTNRkzueekeyuLw5lcUMXn98tfb5MGJkUo5WilJJyZ6sdXtwpXeSvv9TVFMHHNy2ish5obhsuJMGD46cBR3XC2euq6rpVbnoqEJjCYmCKWa/OtT0Dfcxx0v3DHqc2VVTHJ4TJzE5C+L1fE0DKlWzGIjnZgMecAXU+WYXBcN52Rhp2ICY4ul39OzB6SaI7KnAQZ98Ia3w0eegbe+BB975GM8efDJnL8/EBnAHQdfXB1/QR6T6GDKGqMJ1kR6TEYlJtr8WmLFZGf3TnvjkivUsHdYfcZ7/UrB1uvxo3sfBUZXTCaq62ky4AxXSy/lgCIm2msyGjHR65wzXE0IMQl/RRKzOvlVCJGxYGTbEUgpGQhb5te0Ug7A+nnr2dWoFu/qkJIPZypeOPYC5RF4w24lG6bHHWdDQiYYCA9kLeWAIiZDXrUwLuzPHOanyziv2Q976+FQHVyzJrOMA0li4stGTCxCov/XZjl9QdTJr7r+DJmKiUgkZ4pA0mdSDGIyN6h2/XG3uk1nmTgXDd0hYhMT4IFV6hgvPABfe+Zro8b656OYOEs5npi6vaMSNs5XqslzRydeMUFYabSRkRUT4Ygadyomdix9AYrJ3t69zBmChIDeCnj3unfT31TNldfDd34PS3ok33zumzl/vz/cr47XR0rekV5nqkdRTJytwlNFMQmOsj5OBl7peoVVFjFpHMpeOtWf8d5yRUzWtoMrAY/tf0z93vDMLuVUhtWGrLtCjZk4WOfIMuk7mNIqPCIxSQtXm+wME5jlxATy28kMx4aJy7i94PjcPrzu5FCVdfPWkXDB9rlwarsyXM1UbDq2iVM6wC3zr3sPRgaRSNv8WuGpoMyVHGw9WsuwziDR3Thet5crV12Z9blG8pjUh6CjIotiYu0CdfJrpSeHYhJsp2FY3RazyEMxiYmzjAPJRaMz2Gl7GzQxaR1QxOT8xefj95bzpXPhk08pdeDOrXeO+Fw60j9DMXF4TJylnLlW6Uq64NkFiphs79iesXs+3H+Y/9v5f2PeVWcQE5Khb7kyhnqGe2xfQdytLqxNlU14XB5bMQmEA3kf056ePZzQo9QSgDetehM/uPIHbJ6v2ivXdDJioJ0u+abHClR7q0dvF46k+tg0MenzK+LVH+4veoptXsSkxO3C4ViY/X37WWWFHOejmATK1eZhuaPTz1ZMypPExG6Rl9OfmCzst/wlQnkf+/xqynZdSCkmeROTdMVkkv0lYIhJ3rVfSBranGoJKMUEkgbYF4+/OKkx2JMFKSWbjm3iNEsirctTXtY7vVqr7u70l0B2YuI0GeoyzptegfvWwKXLL00pBTkxUimnYVhdcHRJR3fq5FvK0RkmutQCaneSawdXCDQxOeYo5epFIxwP2xfmw/2HQSrJ9kgNrGtex3tPey93roWTOmDdMfjQQx/i44983K47OxGNRwlGgzYxcQkXVd6qTMXEUcpxuvOfa1XEJCETbDq2yX7cre1bOfH2E7nyritZ9a1VY5pQnI2YjBYZnj5ZuLG8EZdw0VLdkhqylmc5Z2/vXpY7iMnyhuWc3nK6eq48SGi6Fy3FY+JzmF+zEK3ByGCKYlLnr6PSU2mXciSy6F0xPcM9+KJqozHkySQmKe3CsjSKyZ6ePSRkgtVdinTkmujtVExA+UzWWXkmZXH12gd8qYpJpAziQq0X05mYOMPVAF696NUgUrNM9vXuozKsrmP682xvfoY67WtWqePowRCTvBSTdEObNr5qLKpdRL2/3iYmg5HBgmPCpwP29+0nEA6w/phKFawN56eYaPJSY5Vy0knF/Or5VHgqVJZJt3pM7aSXUnLPS/dw8T5FXNrqcpdxYBTFZFjtFBqGSTGspl8QKzwV9nvsvDA61QONiVJMfG5f1iyTI/1HqAmrnVC/1VL68XM+Ttzj5iuvgrvugzdvDPLNv32NZbct492/fTc7OnfYz6PfC01Man21uISLal81EUvE8sZSFZNsxASZaoD91OOforprkLvuVSTgF1t/UfBrMBQdAqneh+F8iUnaAD99YZ1fPT81ZC2Pck44FuZQ4BAn9KqSIahkZ/2Y+bzXOu8o3SRf5a0i4lYt4J7YCOZXh8ekyltFrb82dV5Okcs5PcM91Ies109k95jE3Kq05Y2Xpl14Z/dOQMUxPL1AvQeBcCCjfdupmAApvr+GYXW7dKUSE5gZ83LaAg7FBHj14lcDyc4crZgs7VNDZ62B4jYxSciEfV63D7bjjqsNXFfF5LcKgyEmGbXfbDu99MnCTn8EKK/KbDDAau/MacdUnHFdSC2U+bZQ6lJO+uvnEi5WNKzI2pnzwrEX2N+33y7j+Nw+rlh1Rc7nGs382l6lSFVVJLOUU+ko5XjcnpTIaolkf99+tYtwqBrFICaReITOoU6bmAgEJzadaLcLQ5KY6HA1bXxdULOAJXVLuGn9TXzjbPjwZfCezbD3G3Dr32Lc99xPWfe9dXb3VPqcnDp/HZC6SFeHk58DnWegVaKjNaqVdUlf0meyv3c/D+1+iPdtgmtfgsbg2M7/oegQvph6/IS1MuVDTJwD/PSFVYesFaKYHOg7QEImbMWktbqVck85tf5aBMJ+r/vD/TlN8rnyjqq8VSCSA/FyBaw5FZNqbzW1vtrUeTlFNmimK07ZSjlgHXekNKWcnV07Qaq14emFyTEQzk1ROBZmODZM/XCyRPnivGQCbHq4GhSPmJQ6HiISj3B88LhqFa5R68e5C88Fkp05B/oOsLd3b0oZBxQxaU5bY9qD7TQNKSIXdxvFpCQoJCpaJ7+ml3JA+Uy2zVWJg55YpgE2noiz8ejGghfs/b37+ddH/5VvP//tkk/23HRsE56YqrM/uVgtltFElOHY8Ii/5yzlBLKUcgBWNKYSk909uwH4yYs/wRODq3aqMs5lKy7LIDZOZCMm4ViYoeiQknn9VpvvcLKUY5tfI0nFBDLNcdqgmksxGWv5Ttd0NTFprmpmfvX8rBOGdYaJNr5qH8I3L/8mX3ztF9lyajMXvxveei28qg32fwMWdUTsZNhcxETv7HXNvT+i/Aztg6lBS5BUTbRi8r0Xvoc7Lrn5BThcDad0wNaOrQW/DunziiB/YpJ+YW2tbk0qJjLZzTQS9vaq0K7lPbC3QZVxQBHn+vL6lEC9XErhSKUcwO4AzMdjkk0xKXaWSa7XT6PSq072oEWoRivlHBs4xn0v32d3iRQDr3S/Qmu/eu1sxZPUco5+XepDqaWc9ccAOTHEZDg6zGt//loqvlDB5Xdebm+CJhtH+o8gkSwMqFZhvX5UeCpsA2wwGuSVrldSiMmqxlVZR1+0B1Xqa6nC1cAQk7xMac7QJGc2gRPr5q1j2KvCv07syjTAfuyRj3HG989g/ffW86W/fSmvY4vGo5zzw3P45p+/xK2/v5Uv/PULBf1t6egMdqrpvGOcornp+CbWdCop8Gi1urjB6PKys5TTn6WUA7CyYSX761W3iSemFJMDfQf4/qbvc+MW2NQCR2pHLuNAdmLinKHRW56pcujFVie/6sXYnqXhWG+0x0RPXtUhawmZGPOOS180WwbV6zq/ej5zK+dmXTTSiYlujfW6vXzi3E9w4KMHuOONdxA4ZQXXXqM6di7ZB88feR4pZW5iYpFt3TI8EB6ge6ibuIzbxKTSU4nH5eHZVjjrsNqFtQXa+OHmH3LFTrXgPbBadUNsa9+WlahJKdndvTvrznssxCR9srBNTGpaGbDMfzXh/Eo5OsNEm19PqD/B/llDeUNeSb+2+TWNmGjiN1LKdIZi4suimExAKScfxUS3DI9ETA73H+akb5/E1fdezZrb14w6kDNf7OzayapulSuT6z3Qn3HdnQXKg+WS0DIwMcTkK3//Ck/seYwPPJPg4V0P8eW/fXkcf+XYocPVdClnYc1ChBAsqVuS0jIcS8RsYlLtrebEphNpz0ZMShyuBoaYZJjSRoqK1m77dI8JJA2w2nDlVEz29uzlm899k48+DW95Gb70ty/lRQ42HdtEe7Cdu+6Di/fBg7seHMufCMDj+x5n6TeWsubba7ju19cV/PtSSl44+gKnHVN/ox4sBqPv4tJLOdkUk5WNK4m5FeNf1quIyb//6d9xD0f4jz/Dpy9SH7g3n/jmEZ8rKzFxzNDo9WchJllKOZCpmAC2YtJU0cScijlqPssoF6vRkB6uNr96PnMr5tJZodqFdWR0LBHj+OBxlc1hnYLzq+dn/P3vO/197Lh1B7W+Wl6YD6cfVeRwb+9e+72qDecu5Tg9NYBNTBbULGDdvHVJnwlq4F3XUBf/+Dx8+wzY2qyISTAazBhoGY1HueAnF7DyWytZ+a2VSqJ3oFBikpAJ29SsL6w628ZuGS4gy2Rvz16qQ+o8OF6VVEwgf2KiYwXSp5DbKdM6zDHN/BpLxAjFQrbHxCVclJeVZ3pMilzK6R3uzVsxqRqllHP39rvpHe7liZ9AbCjIT178ybiPT0rJzu6drO6CnXNUyU5/3pyG85TPeLl6/RDKZ7LuePGJiZSSn239GRcegG89BJfuUQF8+ZZ1thzfwq+2/aooCpg2uetSzqLaRQAsrl2sSjmOU0YTk2X1y2iubM66+Tk+eDx1To5RTCYfhZhfdbtwNsVk9ZzV+Nw+2wB7bPCYLdH/ctsvEQn4+NPw6oPqA5VPF4dehOYMqVp5+syUQvDVZ77KvONBPvGU6nLZcnxLQb9/dOAonUOdrD+u1IuAz6GYjLJYppdysr1+ujNnt1XO+fOBP/OLrb/gw88qP8vzC+Bzr/kc/jL/iM/lL/MTcSujHjJVMdELcK/fUk/Sckyc5lfITky0x6S5qjnvi9VoyCAmVUoxCXuUH6YmrBaN44PHSciErZg0VTTlfD3cLjentZzGCy2wwapivHD0hRTFJODLXsqpttpzNTFpDqoL9byqeZzZeqYd910Wh7tfupuVXWouyf0nJokJqE4dJ+7fcT9/PfRXvvAY9Hcd5XsvfC/l5yMRk8HIYEYpU7fP6ve12lttt/HbIWs6yyQPYrKnd0/S+CqSc7AgP2KSkAm7HJPN/Aq5FZP0AX5V3iqEENT56tQmYCooJqOUcvb17qNhGF5zQAXUvdL1yriPryPYQV+oj1Vd8Mqc0RUTbX7VnVQ6AdZJTJzJrzA2YvLskWfZ07OHd26BZ1pVIm17sJ27X7p71N99eM/DnHbHabz9/rez7rvrxl0Cautvszv1tGICag6ZNr9qOInJ3Mq5dFeotcAdV6+1lDJjsrDJMSkBqrxVBD0WMZHZ2/gy2oWzKCYet4eT556cYoDd0r4FKSV3bruT8w+qC88y9fnJ2E1mg3MnP2cIu1NlLDjYd5C17fBeq8NTjwPPF/r+px1TxMS5WI7G+gPhAGVxpWIEvbkVE0i2DHcPd1M3JPmnp+HTF8PJc0/mhrU3jHqc/jI/CAhbIWspislIpRyZJCb5KCZzK+fSWN5YNGJSFle7vc5KpYI0VTYBqe186eFq2l+SC6e3nM7WZvV6+qLKSJyP+TWXYqKJSb9fKVsnWdEHt2yEH62HSJnK8lnTqYKtdBS4xl8O/oWakEqp1Z0CToxETCDzYp5tgJ+GUzGZn2fI2t6ezFZhjXyIiT4+rZhUeipxu1TgzWjExF5jLI+Jvn+tX5Vy8t0EFIJwLEwwGrSJiVu4M9Y2fRy6ZXgkxUQbs0H5dLRPbDxwduToUo42v6YQkzTFZFn9MntUyPpjSWJS5a2yyfx4iMkvtv6C8oiKMLj2akXMT2pXAYejqeHf3/R9FvUkuPdu1cark2nHikOBQzQMqzVv0AcLaxUxWVy7mO4K8MShJqRStZf0wf66JDFJuJIt2O2D7QxEBgjFQrZi4i/zZ73eTTQMMfFWEXerToDyHG75/nA/rgSUx9TOIZv5FZTPZEuz1TsvVTln07FN7OzeyQ1b4ZenwNI+dd982omd+RqNQ+r7sbLrvlAf9SFFjHzRwnczm45twpWAU48rt3vKYjmaxyQUSHYqiOwek8aKRhrKG1TLsLXefPIptQvfNQe+cNEX7EV+JOhFR5dzUjwmI5hffTE1sC3uHkUxCSZ7+4ummAweZZ41sTjhgpbqFuZWzgVSA5AKJibzTyfsUWRvbXuSmLjjioQNekf2mOQiJpA0wFZE4F1b4Hsb1PyiQZ9VBunJVEyePvw0Zx5Ri062iPVcxCQ99E1jpHCwFMWkXymYI5mT44k4+3r32cZXSPOY+Ed/r52xAundeynm1zwUE30xqPXVEipTXglvrLiKSbqSWF9enxE9bpdyPLm7iTQO9x9moXV4K7qT+SPjgV6nVluKSZ9fvUbueKr5NV0xqffXs37e+oxSji7jQPL90R6e/nB/XiX2aDzKXdvv4sqdKnDwUJ0qY370GdWNNtLIAlBr/8kdcP5B9f3BwMFCXpIMtPW3pWSY6FLOkroldpbJ4j7lYevzq+F9upQDjjVmqCNruNpkx9GDISZ5mdIGIioqOuhRffC5ukLWz1tPZ5XaXSzuUwbYO7fdiS8Kb9kBX3i1pZjI/IiJc7GaY+0SsgUL5QMdQ+6W6sK/o2tHQb+/6dgmVnarkzVQXqDHJJI6WTibYgKpw/wWBOCmzfCfF8C5C8/ljSvfmNdxZiUmORSTUCzEcHSYYCSYMlk43fyaSzFpKG9Qg+OydAkUgvQME21+Bewsk2zERKsCuaDl7Bfmw+nH1HvYO9xrvxfSlVsxGYgM0B5spzIM7oRSCudVzWNl40pqfDU816qG2123Hf6+UC3O/3TOPwHJco6TmAyEB9javpVXWZlvutXcidEUk5GIiR7gp1HhqaDOX6c8JgPKw5E+2t2Jtv42oomobXydUzEnhUA3lDeoVvewUoOyERNn915/Wvee/jqnYhJJVWWdigliYubljJb6ClnahUco5bQF2ljQDxGXIqahWCivbqiRsLNrJ+UR9Rk4WKfOWb0pylBMZFIJrC+vt0eFtAwqQ3NXhQrg0/C5fXhcHvsciyaihOOje0Qe2fsI3cPd3LAVfrFW3fbdDfDWHTAnqFSTkXCw7yCLAjB3SJVDjw0cG9Nro9EWaGNRIDm8z1nKAezOHGdHjlZMIHXzkxGuVgJ/CRhikmFKy9Uu7HTa55K21s1bByTrmhuPbuRX23/F5bthyzx4pUktunOD2adjpiO9lANjK+c40z5B7T6coVv5QCe+bmpR3/f5C/OYaOMr5CZ2TmLymT/DHafDsRr44iVfzJu1ZxCTuFJMRMKK0Pdn1qmD0aCd+gqppRwdiY6ESmvNCvqSikmvPzOwrVCMREx0lokmJuURpdx1V4yumJzQcAI1vhpeaFEG2L5QH5uOb0qJo9ck0f4c+JLtrEcHjiZrzUIRE5dwccb8M3h2gerM0abX+dXz+dSrP4VA2MRkb+9e+/P0/NHnScgEr2pzzH4ZRTEZbZbJaBdWO8skj5C1vT3JVuE9DallHFCPnXApwpF+UdQYqXvP+fpmm2SuXyddytFERr8/+jUrZrtwXsQkvV04RyknFAvROdTJgn6lpmnVc3f3+Mo5enjf3vpkto02wKaYX0O9VEWU8h0tU4qJHhWybS6ccTRTMRFCUOuvLXhezi+2/oI5QTjvEPxmtVr3uyrh1yeqsuaDOx+0z6d0DIQH6A312lN/5w0qxXQ8OBQ4lBKuZpdy6hYD2AbYvIiJpZjMGyxdHD0YYjJq7RfUjj9baFI61javRSBsA+yenj0cHzzOO7YlmfX+OusEybeUI9VOZTzEJN3weGKnumjk6yDvGuqirb+N9Q5iMuRRBtOyeH4eE2enQq44+ZUNKzlitSFfuRO+eC5cuepKzl10bl7HCdkVk57hHqqtjJKYO2l+BbWgpV8QnaWcaBlErTKfM8NEKybRMvVc1eHiEpOmilSPiX4PWvX9xOjExCVcygBrKSag2obT5+To+1Z5q1IW6T09e1IyTPQidWbrmWybqwyO9cPwyAlw82k3U+OrYUXjihQD7PaO7QD8ve3viIQiM48ts3b/oygm86rmjXjRyDZZ2InWmlYO16huBcj0tDhhtwpb5ldnGQfITH8NjVzKSScmTuWhylIenGUOTVSc5ldIflZKrZiM1i6slZGF/fCnpaqUA8nXdazQw/teSfKJrKGGfaE+u1QL6rxe35IcFeJJZBITyE1+u4e6ufG3N3LOD89JmT3VH+7ngZ0PcO12+N1KtUm57dLbWDdvHV8/WxF1T0xy27O3Zf17dL6LPidbBsanmAQjQXpDvXYpx+Py2GbV5spm/GV+u2VYExOBYHHt4pEVk2Dp4ujBEJMMYpLL/OoMPsrlMan2VbO8YXmKAbZ2WOVI/PpE9f2+eliaLzGJBCmPqjdJt8iNl5g826pyVhIykbc5zZn4qokJwtrFZbnApKM/nF8pZ0XjCqRLeSK+eC4MVLj4wkWFZbfk8pg0DCeDl7IqJjlKOZAsJzjn5DRXNduy8EgXq9GgiZMmJm7hpqmiCV+Zjxpfjb1oxGWcbe3bsoarjQRtgF3VpbxFcRnPSkxAKYHaYwKqZdtJTPSCd2brmUTLlDL43Q3gcrt53+nvAxQ5z9aZ8/Thp1nTqUpTuxuyKybBaLAgYtIz3AMy6StIv7CualzFK3OUcdKVgG0d23K+Tnt79+KPKnWqrTa7YgIjJ/2meEzSiInb5aa8rDylA1B3g0FmKcfpMYGJmTDsJCbZXj+Aco/60Oh24VAslDXoUbesLuhXpb25QfBHx2eAdQ7v25lGTBqHMrty6kLJz3h9eT0LaxZS769ns7VmFUJMPvuXz/KrF35G+LlnuOE3N9gZJffvuJ9QLGSXcZbULeHcRefysbM/xkvNyvx97Xb40Ys/yvpeaWKyOKCUn/kD+YX/5YLOMNGlnNaaVtUqjVKEFtUusjtzNDFZULMAX5mP+vJ63MJtrzH94X4O9h3ElVDnRKcp5ZQOo5nSIDPNcSSX8rp562zFBFTd8bFlypcBVqtWrzpB02c9pGMwMkhlFBI4PCZjGBZnpyIOq0jnE62u43zLOZuObQKJnWGiFQVd6+0L9434+/mWcl6z5DVUeCq48nr4+tnwD+v+gZPmnpTXMWrk8pg4d1Pa/ApqcRtJMYEkMcmmmEDyYjUWj4neLWliMq9qnm3ynVupskx0zsArXa+MiZiEPKoN+xTLYpGTmPiqk9NWUcQhGzG5cMmFNJQ38LZr4GvnwDvWvsPOU1k7dy376tUFviakiElCJni67WnOOaxmnejdfyQeSTFzF6qY9Az3UB1W73W0LNU/AHBq86kjmnGd2NOzh6W9qh6fcOWhmGTzmDjyjrLN1LLHX2TpMsrWLgyTrJj4M4mJDhJ0Thh2EioNp//pQJ36t6x3fIrJ3t699vC+V+Yo0g7Yvq70HBPnnJx6vzLyrm9Zz+Z5yvcy4MufmDy671Eu3w3Pfx+u3wqfeOwTfPGpL/KLrb9gebe60D+2DN5xyjtwCRfXnnQtzZXNfO1s1To8GB7kh5t/mPE3aaProoCKQWgZVMbssUITHV3K0cZXDR2ytrgvtVUY1HvbVNmUkmWyrWMbc4bU+hArURw9GGIyqikNrKhoh8dkpEj09fPWs79O7W4ahuCGrXDnKWqRbaposolJXMazTn91QnsfjlepD6JIjF8xeWaB8nC4Evl35mw6vomlveo16qyC8xadpx7Xn98uLhAO2JOFIXcpp6myid9e+1vWn3EFHzvvn7n9Dbfn9wc6kEsxcUZVOxWT3uFeZX7N4jHRu1VbMRlMTUPUF6vuES5WoyFbuJqGTn9tsq4DEpk19XUknD7fMsBaPhPITUz0Iq0vnIAdTS0Qdgtznb+O31z7G8484yo+cM6H+Pbl37bvv7Z5LQkXvDRXtVBubd/Kru5d9IZ6eVWb2k1nG0qXkAlCsVAKMZlbMXdkYhLKPsDPeSwAW5pVN1l6+7ITe3r25GwVdj52PopJrryjal/ulOn0dmFNavT7k+2zdvf2u7n0F5fyH3/6j5yze0ZCz3APZXFVoun3ZVdMIG3CMNnXSGeWxuEaRYTH2zKs1yfdKqw9fNneg/TJwjpo75wF57BlHnz2AkAkYwk0shGTUCzEru5drG1Xyclf+SO8fSt88vFP8vj+x7lhK9x1surge8cp7wDAV+bj1jNu5eHlqux7wQH45nPfzOjyORQ4hCemNpovtKjPfddQF5F4ZEyvkb6G6FKONr5qLKldkmF+1cQEyEiY3taxLSVcrRQZJmCISV4eE9v8OkopB9SHR7rUYvjGXUrS/sMKuP7k61nesJz99fm3DOsSQ59fLda14bERE2dcc1uN2nEs7su/Myfd+PqaJa8BkiFrI3lMpJQEQgF7sjDkLuUAvPaE1/Lg9Q/y5dd92Q7LKgT5KCZjLeU4FZOmyqaUi1XjBBKTuY6yviYmtb5a+9wdCcsbllPtrU7xmeRbyoFkq3BTZRNlrjL79vMXn89vr/stt112m/16QZIMODtz/nbob4Ca3fP0QrIOpRuOqjdEE5PysnLq/HWqrGFlDGVTTLIN8NM4ae5JuITLPpZ9vfuyDumUUrK3NzXDxBmu5nzsUYmJzN4uDFbKtIOYOI9lMDKoIgmsvz+r+dWhmGzv2M4Nv7mBtqcf4bN/+Sx3vHBHxvGMhp7hHvtckK7cxKTSU5mimGTzmRzuP0z9sDKfDvrU6zjelmE9vE+Xcs5sPROXcNnmV+cwxWyKCcCHzvwQK1pO4vMXqHXripWpA0CzEZMdnTuIyzindMC9J8Fr3wVf/iO8Ywsgscs4p7eczolNJ9qPdcuGW/B6fHxvA7xjm/I0pTc5HAwcZEE/HKtSn+MW6xTQrfmFoq2/DVdCKS9HshCTxXWL6ahUn6u6kHredGLSXpVcYw73H06No59tpRwhxKVCiJ1CiD1CiE+W6jjS3fK5SjnONMeRFBPN6l+cB5/9k8rhCHsUs15Wv8xWTGB0YuKcndFVoeqq41VM+vywY47ymeRDTAKhAHt69tiJry7h4vzF56vHzUNeDsfDRBNRu5TjcXlGTW8dD/Rjh925FZMBr/qglsVHN79Cpsek1leLv8yf18VqNDiJybE0YtJU0ZRBTHQcfT5lHHAYYLMoJgKRQrKztUc7M0zyweK6xVR7q20yEAgHuOfle2gMqkV4+9zsikm29N0aXw0JFwyXWbv6HMQkl2JS4algRcMKtsyDUy3PSzafyfHB4wxFh2zja7W32jYfa+gduH6ve4d7My64/eF+/DGIC1VaykZMciomkQFbtZOu5LrkzNqoCykyk5AJ7nnpHmQ0xtM/UO/rAzsfyP6GjICe4R7qR3j9NCq9lXa7MGTvzEmf4bS7QXXmjKdlWA/vG/BBvx/WNK2h3p86TFFvurRiogm3fr+aq5p58ZYX6fqXLh5712O2Z0ajxptJTHTJb227Itgvz4VL3gVfehS+9jBEXaoF/51r35nyWE2VTWyYv4HN85Ll8vR5QYcCh1gcUCXDo1b4H4zdZ3IocIh5g+o9jJRlL+Ug1PMdqFPnVjbFpNlx2UuJo59NpRwhhBu4HbgMWANcL4RYU4pjGU0xkVIyEMmvXRhUOFZzZTMvzlMGpztPUSa801pOY2ndUtpq1GLvieWhmDhKDF0VSv4bl8fEujjvaFItwzu7do66m9Hyt1ZMVs9ZbV88bY/JCIpJtjj6iQzsGUkx0QuwdCXbnXuGe3KWcnIpJtrNno2YFDog8ejAUXxRVT7pLs9UTLotQiqstynfcDUnTm85nS3z1HvujSWJSa2/1jbKQdJjUj0OYuISLk5pPiXFAPvHvX/k7MMqjCrhyq6Y5CImkDuZczRiArnNuE44pwrrVuH0c7TMVUaNr8Z+ryUyo4SZMScnl8ckCzHJGOBn/a7b5abKW2WTOYlkIDzA4/sf54yjUBNRf9tIZapcyOf1A0sx8Y6smLT1t7HQQUz2NKjXE8beMuwc3gdqHdWhhs7012g8ymBk0F7fBCKFFJa5ymisaEw51zXSyXggFGBr+1bKI6o8sqsRLl1+KYdaK7n4RpXb8/NT1fty3cnXZTyeM/IAMomJzjA5VKs2Ii3WKTDWzpz0cDXdKqxhZ5nUprYKa8ytyFRlZ7NiciawR0q5T0oZAe4CrirFgZSXlSMQtiktFAulmFL197pd2Ov24ivzjfiY6+at49kFavf15GKllgghWFa/jLhb7XgXBUbPMnGWGDQxGati4omp9t4hj6WYdMJwbJiDfSOnDmrj6+lH1UCs9fPW2/JyPh4TfeGpDeWeLFxMpBOTvlAfw7Fhu/NAo8cywBZifnXOyQFVV670VNoXq7iMFzyh9OjgUWWAq1aEKZ2YxNzqQq53iGMhJhvmbyDkUReLU9oz4+g10nePYOUZVBZWa147dy3b5qrn0oTqVW3K+AqpiokmtXkRk0hmu/BoF9ZTm09lf516r+uGsxMT51ThvQ2ZZRyN9KTf9E3CaLECoykmzs4/Z5kufcJwW38bzx15jov2q/uvbU/NoMgXeRMTb6XdLgwjKyY6S2N34/hahp3D+3Sr8Ko5q7KGGjrN/b1ZCPdIqPHVECpTwZPemKWYdGxlTaciJTE3vGfde3joHQ/RNr+Sk26FL78Krj/l+qwX7VWNqzhWrbKG6oZJGVQZS8Q4MnCExX2KKBRDMWkLtKVmmKSXcmqTWSaamDiN3XMr5zLoVX9/hfX+6s+81+0dsew+kSgVMWkFnM7Pw9ZtNoQQNwshNgohNnZ2dk7YgQghRl0wINOUNhLed9r7eHkurPogzKlq4r2nvRdIMlVdzslHMdG7qO7ysRMTnfbZ5weE+qCfaD3MSOWczmAnf9z7R+YPgEBdEE9rOS0pL1sek4HIQM4OI2cLZa7JwsVEOjHRgw+dpRxQX2uVo1CPiVZMgIyFstByzrGBYxkZJhrpOQOemHqe9qrRU1+dsA2wls8kFzGp9qV5TGRy9zSvsgBi0ryW3gr1fuvJpuccVsZXSFNMRinlQHbFREqZt2IiXaqEdEoOZWFPzx7K4qqz4UAdLK9fnnEf/fgjxdKnd+9lmF+9qeZXZzRBhmLiKLGlTxj+3a7fEUvEuHifmlGky1QjdR1lQ6GKiT7udMUkHAvTEexIKeW01YyvZdg5vG/nHHU+LKhZQGNF5nyqlDj68qS/JB/U+GpAJEcf9If72da+zS7jgDqHXr341Wy8eSNvO+9mPvGaT/OdN3wn6+OtbFwJQpGaFd2wqyepmBzpP0JCJmzFpKNS/R1l8czOHCkl33/h+7zxl2/kq09/NWuLtpSSQ4FDKamv6aUcPd7izrVqJEprdWtKZ9LcyrkgkkGO4NiAlSiOHqaw+VVKeYeUcoOUckNTU9PovzAO5OOW16WckYyvGm858S384e1/4DOXfI6/vPsvtFQr1+jS+qVA/sRkMDKYUsppHB5bS2pfuC/F8LijyaqBysyW4f29+/nMnz/DWT84i+avNPPQnoc4+7BlfBWKmLhdatiXc5BfLqUgvZQz2YqJRJVWnOZXSJZf9MRe/Tp73V7b5Okr8+F1ezM8Js66azZpuRCkh6u1VLXYP0sPWZs/oMoqCVdhioltgLV8JnWW3ydDMfHVEC4DYe0e64eVvyPkKUzSTTfAuuNqwvEzWRSTsZZyBiIDxGXcHuBX6anMqmSeOu9UANtnsq19W0b5cm/vXhYF1HsQKctfMclFTHJ171V5q2wvG2SuM87Ov5EUk9+88hv8UTWr6PYzrDKVnEBi4k0zv6YpJnpys+7IAdWxoluGx0JM9PC+1V2qlLOycSUu4VIbgfJkrlP3cHeKh67Xn/SX5IP0c2x3z27ag+02MfGX+e0OrdVzVvO9K77Hf130XzmN585hpKu6U0s5zgwT3ZbeWaGIQLpi8tdDf+Xm393My8/+nn965J9412/flbH56xnuYTg2bJdyKj2VGZ9pl3Dxtdd/jU3LK9h+QhVfe/3XUshG+uYHktPES1XGASgb/S4TgiOAU3NaYN1WEqS75Z0Lxkgx07kghOCyFZdx2YrLUm5vrW7F4/Kwvz7Ksl71oeoP9+d8zGylnGA0yHB0OMPENRL0nBxNTOwsjmBqy/C29m2c8f0ziEbDnHUYPrsbLtujJO6PXKZqtdrcW+evI+AfSBnkl21hc5ZyAn5YksfrNx6kExMN526qN9Rrp78+Y+UvVERVOUWXcTRUDbqLZb1q4eopz1RMxjPI7+jAUS4ZRTHprFAtw1G3ct5DYcQkmQD7F97zopo22ueHZemKibcaRDKWvmkoM8MkH5w892QgSUzaatSOLlCupOW2xEGqIqplPZdiUpWFmLQ7iIkzg2Nbc+6L6sKahdT569ja3MdpxxShOdB3IKXOrluF91rXs/RWYY2G8gbaRnivB8IDLHB6TNI2MSMps4ORQeZl8ZiAIvNd/iSZe+7Ic1zUpl7f3Y3KbDt/ALZ25E9M4ok4gXAghZikX9Ts4/aM3C7szDBpq1EzaMLxsO0zGUspR5dAdOrrWXNWA2Sd6J0+WbhgxYTkOfbM4WcAlfnz0ApluHV2o42GExpOQCDY1ShZ2Q2/CByy12tnholWOLTPJF0xeWTPI5TF4ZVvqaygT/JLYokYv3jzL/C4PQRCAd7zwHsA9Rr/bZHyl2RTON5+ytu5es3VAHjcnpSfZSUmVilnfomMr1A6xeR5YIUQYqkQwgtcBzxYomPJq5SjWwDHMwLa7XKzpG6JSn/tU7ft783tM8lmfoXCDbDpcc2IpGriLOV86e9fomIgzMGvwXd+D2UJ+NjroekT8LN18M/n/LO9eNX6a/Ma5KcvPFrinuhSjs+trgoZxMT6+/Vu2O6usGRgTQC18VVDm+P0EDDpSlVM0qXlQt6bYCRIIBywFROPy0NjRTIkLH3RKDRczYnTW05nS7N6z5uDuUs5gD0fKFu4Wj6o9deypG6JTUx0fgnAZcsvI+GypnSHx66Y5BOnDmqTMJoBdm9PWqtwfQ7FZJQJw6N171V5q4i41aRgT6xAj4kvqZgAXLQfnlgKiOxDE0eD/rzq16/WV5tzeneGYpJWykkfLnnOwnOApM9kLC3Dr3S9kjK8b1XjKnW81jDFyogqgWSUcsapmAxEBkCq3JutzUn1L1/4y/wsqVuiVB5rKdCK0aHAIZCpxET7TNIVkz29e1jSp9JXL9kH//sI3LP9Hq779XVsbd/KWT84i4d2/B/f/L3qfnpyMZzUlDuM0uP2ZJASSKoi6YpJewGG94lASYiJlDIGfBB4BNgB3COlfKkUxwKZxMSZLzBaaFKhWFq/NK+W4Ug8QjQRTXpMKsY+LyddMQFlgF1ttQxLKQlGgvxmx29428vqIrLuA/Cp18Lg2ev5xAX/xrPvfZb/vuS/7d+v89fZHhPI3TKsXz+7lDPBxEQIgc/ty6qY9JQnfT7OCwykXhCd0MRkeU9q6qvGaBerkaB3SZqYtFS3pJj2GisaEYjiEJP5pzPsVeZOm5j46jL+VrDq7ZGxExNI7YbRxGROxRzb72IbpyeYmEDSjHtSh1JpthxP+kz0hU0bX31uX87guobyBjs1WCQK95hUeatAZO8AHAirCeZ2559DbVHqZHITAHDxPnjcEn22zFOv88udL+cdtFbI62d35Vh5MumlnLaAFa5mnZ+nNp9Kvb9+XC3DenjfngZV8lhtKSYN5Q0gkunN3UPdKYpJn398igmo814Kde6vnVsYMYHcnTkH+w7SFFSkfMgioMeqss/L0SredqtV+bxDcNtDcP/L93Pqd0+l9+BOHv+pKgud+T6Qc5v4zwv/s+BjTS8Xi4S6znSUcE4OlNBjIqX8g5RypZTyBCnl50t1HDByG5+dyFiAx2QkLKtbZg/yg9zExDlZWJdytI+hUJ9J73BvJjFpUgbYnuEeOoc6+b9d/0cwGuQd2+DOtaqkcPTjR9n0/k18/uLPc2brmSmPWeevS/GY5FRMwgE7dKoYxC4f+Mv8GcREz8ppqmii2ludEksP2MqUMywMksRkUX/qnBz7cZ2lnAInDI8UrgbJNsd0YqLDxwrB6S3JBNgEameeoZhYaqCOpR8XMZm7ll2Nyndw4QHVkfOqha9KBobpDJwRzK/6s+YkJrodu5AL66nzTmXArxbbE3pSSx7pU4VPaDghZ0dHQ3kDMbcVgBYZwWNiXXSymV8h+1yuwcigmuo8gmKiNwE1ITipM9nlpAlgJB7JaE/NhYKIibeSmBviLtXZl00xqQtBzAUDflU+W96wfMwtw1JKdnTtyGgVBrLOp+oN9SZnJo2zlAPKJL1tLiDglOZT8n4sjZWNK9ltERORSBKTQ/3JDBMNrZh0DnXa6a9SSvb07FFqUwP0lauQt9OPwnd+B2cehufvUMMSr7oOVi7bwAs3v1Dw+A5Q722lp9JeYxqH1WsRc5fWYzJlza+TiXS3fK5STrb5F4ViWf0yuivAnVDtZLlahvWHP1spZ7yKycrGlXbLMCgD7J3b7mRBQMWIP7RcJdVq0242aEOe02OSDYFQQA3/KlOGuIk2v0ImMREJ9f7p3VS6LwRGL+VADsWkvIFImUq8rMpysRoJulV7UUC1kKcTE1BEqtNyzDtbhQt1y69oXGEnwAb8qiSVzfwKyQ4FPfrc4/IUtNiDUkxibtVR4YsrM+A5C85Jzn7xja6YeN1e/GV++6KRkAn7fqNNFk4/FkgaYJ2KiXOq8J6G3GUcGDn9NRwLE46H7bZ4l3BRXpbqA7PDHNMUEymlIia5Sjn+WsKWCu+LwvkH1TDOsIeUMDvIP8+kUMUEHBOG0xWT/rYMNW9F44oxtwz/79P/y77efbz6YLJVWJtKnWMgdDNA73Av5VGQKKN2IaTdec5rRSq9I6dQrGxcSb9fvZfzB1IVE2cZB1KzTHS7d9dQF/3hfpssl5eV0zx/Ba9/pyKkf/w5fPgy+Mxr4F3rb+TJdz+ZkV9SCJwJ01MhXA0MMQFGdss7SznZYqYLxbL6ZSBGnzKcPtRrJGKyu3s319x7Ddfce03GziQUCxGOh+3dhMfl4fSW01Nahp869BQP73mY67epKcjRsuQMiFywFZPRPCbh/OPoi4V0YlJr7UQTLlV/bihvsM2vGqOVciB1To7GeNJfd3bvpCyuiMneBljRsCLjPs5FY0GBqa9OuISL9S3r2Tg/6TVKJ4m5PCbzquYVTIScnTnPLFBEqFDFBHIPWdOThUeajKtx8tyTEQj7Ar63d6/9+Xpoz0NUhdUskX31uY2vMPJ7rX0WzmGM6a9ZrjDHoegQEml/1v1l/hTDZfqEYV3GKXOV8c6172THHKVMeGP5+0wKVUwgOWE4m2Li7MhZULOA5fXLx9Qy/MArD/CJRz/BNdvhil1w+5kqSl4fg/ZgOd+D9GTn8XhMIElMmiubUzYh+UKrOzvnKNVkV/cuu7VXZ5iAUpayZZno10oTkxWNK/jzu//MgtbVvO6dsOZW+N0aN7ddehs/vurHBTVCZINzjdGbETCKSckxovk1PIBIqJ3C4DjNr5B/y3B6KUd/ELMN8rvhNzfwxPP38qfn7+Ud96cSivQ4+jp/HSfOOZGDdao0VBWGrz3zNWKJmF3GWT1ntd19kwu1vlq1ywgBcmSPiXOycCkUE6fxt95fT315faZikquU401VTLxubwo5zZgwXID5dVf3Lpb2qk6bSFlyQXPCuWi0jiFczYkrV17JMwvgDdYpcu7Cc1N+nstjMhYT3PKG5dT56/j1ifCzU9V7smH+hhEVE1dClQrCZfkRk6qI6lQKezInCztR4algReMKe5gfqFkzxwaOcdf2u/iHzfD7Faruf/HSi3M+zkjExNkKeijLlFfIPcnczkrS5eK0NSZ9wrA2vp7VehavWvgqwh61npzYOUHExKmYRLN35eiOHFDdISsaVxTcMrz52Gbefv/bOeOw5Ft/gCuvh+E5tdx+eXKYp62YWKVtTUx0qzAUVsqp8FTgEi6VSq1LOR2q02ssZRxIbRle2a02IDovSSsmFZ4KTp57su0xgaTnTKtLziTi+dXz+et7/srN536Y8191HX99z1/50FkfKkrOyNzKubRrxSQ4NRSTUrULTylUeasIeixiIlNrv/3hfrVL8KpdX1EUE2C/RUx+13eAhExk1LXTSzkxt1rQasOpF7/+cD/PHXmO//m7kjI/Vfm8SjK1FnZtDEshJk0nknCpD87qLtjo6+akdrVI/XURfNZKqh0Jdf46Ym5VoqmMjKyY1DoUk1J4TLTxFZKKyUsFml8hmWHifG2y7eA07t9xP4/te4w3r34zrz3htRnHubNbRW7vsq6p6ZNPIUlMWgbVgLejY1RMAG4981Y6hzp58fiL/PupN7KiMVWhcXpMqsPJycILx0BM3C43//Wa/+LD4Q+TkAm+/JrPUeGpGFEx0QPsEHkQk9DIA/zSsbZ5LZubdyVLHse38LtdvyMei/KRZ+Adb1UXgPQWfyfSiUmb4712toIerIPTrcRNJ9InmR+yLvDp6mh6RoZTMVnRo57jhRb49NKLMzJjniiAmIhEcl0Y6fXTx6MNsE7FJBwL0x5st0s5AkFLVYut/jmH+Y2EowNHueJXVzCnc4jf3AX/cBW81OLmoavvTRmUl20jYHcdjkExEUJY51gfzUHV6bOqC15qgg+MwfgKipj5y/zsagyxqlu91puPbwYUcf3rYtU2P796Pi9mUUz29OzBbSmp++rhKuu1nFMxh29c9o0xHdNImFs5l43OUs4UUEwMMUF98OJu5RMoj2Z6TPKdLJwP6vx11Pvr2Vffy8kdasjdsYFjGZ0A6YoJZI+l1z6Fpb3JSPX2wXZbmcmmmGiHu24Z3tgKb98GvzpZka/rT75+1L/DuYurC43sMal1dCqUopTjXLQayhtUlkm6+XUEj0moTA3uSk991Y8HyR3cNuti9fCeh3nrPW+lbhi+u/G7bLllS8oOLCET7O7ezSVOg9+c7IpJr9Ue2VWhymyFpL6mvy7/c8n/5Py5vgBpIqAVkw1j3DndeuatvGn1m5BIm0zp+r9WTPpCfUgpc44FqPZW22ZcSFVM8gkH0zi1+VR+XX8fjcNQOwzPHnmWB3c+yFWvqPf1mYXwzbM+MmKU+UiKycG+g4hEMsvjLVmISfrAUG2stw32Ol3al10x6fPDm15RraFxN1y09CJWzVmFx+VhS3OUte3w84EjdA91p7SdZ0PPcA81YUU24u48SzmWYuL0mOiL6cJ+eGqRUtc8bo9dEtvdqHb+j1gtw9le36HoEFf+6kr6O4/w1C/hy+fC71bBdy7/Vgahr/XV4hZuesrjNAyrtboj2MGSMSomgE1MasKKRLXVwrB3bP4SUGXTFQ0r2NW4jQsPqNse3fsokGwVXlS7iPnV8+moVF4ZdzzZmbOnZw+LAuqzFykbubxYDMytnGtfW/Rnfiy+smLClHLIdMune0yc2QTjLeVAfi3D6bsoyE5MDvQdAFSNvNlaL9qD7fbP04lJfXk9KxpW4BIuu2UYqYjJL0+BsxecnTP50gl9gdHD8PrCfVnvNxVKOc45Odr82utPdtKAuvAP5SAmOrLaOSdHI9fF6uvPfJ1lPdD2VSiLSe7aflfK7x3uP8xwbFjVoBvVcWUrRzRVNCFd6r0fa6twvnC73FR6KlXHTkgtmJ0V48szaK1pTTlef5kfj8tjKybRRJRQLMRQLPe8Il1agrETk5Ro+g742Zaf0T3czceega+eo87nd69794iPkT5h2Dm0UU957fWr0tJopRznOpP+Wc8o5ThUpqteUf6S8rJyzl5wNl63lxObTkwxwGaboJwOrTjl8/rpz8RgFsUkPcNEmzAbKxqp99crxWSUluEvPvVFNh95gV/+Gp5eCF8/Gz5y1ke4ZcMtGfcVQlBfXp+S/rq3Z2/WycL5Qpela8LqNdxm7T3GWsoBpX46s0we2/8YgO0xWVy7mJaqFuJu9dluDqYqJiscuTqTQUyiZer9Xd1lKcNVpYujB0NMgNxuebCCj8K5Y6bHgmX1o7cMp5dyIJllkpOYpLm7gYwBV3X+OnxlPk6oP8FuGX5Vm7ogbJkHbz/57Xn9DemGvJyKSVoppySKSZoxrqG8gbBHtTdWRAGp/g96M0s5ujPp9yuUrLo4bSesdxXOi1VnsJPH9j3GtduhKqrSK9MvFtqpr2eBrJqzKutC4AxZm2hiAmq33u9TXSo95Wo3XcygJSFExuyXQDgw4iDFXB6TQhUTSJY84jLO6UfUDvb+E+Hm027OGTOu4S/zU+GpSBnaqMu+BwMHU1pBF9flVkz0wNBcHpP043CqTHOHlL/kvEXn2RH8+UxQTkfPcE9KiTNf82u6YtLWr0aeZRsuubxhObtHaRkOxUJ8e+O3uWKnKld+8HK4fOXl/O/r/jfn8aSnvw7HhlM/42NSTJLEZGuzUj3WNK0p6HGcWNm4kn31ql3eE1P+mYqIev06K5OKCTiyTAaPIaVkd8/ulMC/ySAmoNaYte3JOTmlhCEm5N7JQHKUebFKOaCyTA7UqZPWlcjeMpyrlNM4lOoxOdB3gIqIWrCyKSY6FdEu5VihWic2nWi3DL/dMr26XW6uOemavP6GDMVkhORXp2JSEo9Juvk1jUx445AQyseTbn69bPllLG9Yzo1vgVhtFTetvynl5+WecsrLyu3HiiVi/OTFnxCXca7brnZH2VI5deS2Vkyy+UsgddEYSxx9oajx1TDgU5L2WDNMRkO2VvNCiImUkuODx5kzlD8xWVS7iFpfbYoB9mPPwDfPBMrcfPDMD+Z17LlGEBwMHGRxX+5hapCqPOjuloRMZComOUo5AT90VCjVx2nSXTt3LUdq1Hk8dzB/YlKoYmK3C6crJhJ7XsuC6uS5md4ynM0Ae9f2u+ga6uLDz6qpvZUVtfzyLb/MmUKrj1WXTjWcn/FCVVnnOXZKhyImqxpX2eMtxoKVjSuJlimytqxXzeyyW4WFIq560+NMf+0Z7qEv1GcTE3+ZP2uMQDHhXGOWBJKKSSlhiAkjE5PRYqbHgmX1ywhboWmt/eMs5QQOsLgPDtSqrAuRyK6YpE+UPXHOiexuVErLNS8pf8klyy7J+4RM7xTI1pUTS8QIRoN2BoxAFIXYjYZcionH5aHCU5FRfsl2QdSo9Fay+f2befSdj7Lj1h12cqkT6bH039n4HdZ0qO9/uF4Rk4OBgymq0q7uXVSHlGpwpBpWNoxMTDotxcTj8tBU2TSel2dEVHvVhOFlvUl3ftGJiT81Yr0QxWQgMsCu7l30DPdw+lHVPVHpqRz1vE2Ppp/fD5fthh+cBlefdHXeORDZiElCJmgLtCnjq3VNTFfWQBH/Ck9FSgfgUHQow2OSrpjo0k7Al4yhv2jpRfbPT513ako0fT5ZJgURk/R24UgqMakNKWI/4CfldUxvGU43wEopue3Z2zi5XamKv14DN62/aVRikS2HSH/Gq73VBc22gUzFZDwdORq6w86ZAJs+BVgTjqOOeTnpHTkn1OcO/CsWnMQEjGIyZZBOTJxdObb5tcgeE0h25uQq5bgS4IvBcJr5dSg6ZOc+HOg7wJI+FUQ05FEf0HSPic9KqQ57UolJpEwZvXY3wP6G0bNLnMhHMdELri7lVPuqJ/xDBtkVE90SKYSwF2FtgHWWy9I9JqDOj0uWXZJTqUifeLq/bz/Xboe7T4YX52Wv/e/s3smKHvXaS1d24yuohb7KW8WP18H/rVQL5kS+hnqR9iYmXjGxSzmjKCYR6zrjjamNwpMHnwTggoPwl8UqHyWfi9Ha5rVsa1Yhgh95Bn5+qhos+LGzP5b3sWcjJh3BDsLxsF3KqfXV5ry4pg8MHQgPpGxCsrULu11u1s1bx0/WwX+8RuVfnNZyWsrfBclo+u0d24kn4iP+HWNWTNKaA7KFq2mM1jL8t7a/sfn4Zj70LHxnA8TdglvPvHXE44bkRqDRSUyGC5+To6HP+dZ+9b7urxtbFL0TWgHVWSZASobJ4trFqsMPwTFLMekIdtizy5b3WLOG0jrnJgLpxKTUcfRgiAmQ2sZXnU0xCRdfMYFklkmuUo69UFvWg+5yxyA/K/lSE5MDdRbTHcwkJtnCh3RnzpZmtUCXl5XzptVvyvtvyOYx0UZAjfTJwpNRxoEciolj0Uo3MVY6LojppZx8kLGDk3DddrjrZHLW/nd172JV18itwqAu0F9+7Zf5yyov7Uvn8MVLvljw8RWCal+1TcI1MSm2rGsPgMxTMYHUWPq/HPwLLf1Kyt8+Fy5YfEFez3tq86n0+5X69MHn4LazVJZL+riFkZCNmOjOOF3KyVbG0ciWmaQHx+lI+mxelx9c8QNaTjmb6lNO5xdv+UVKqaO5spmmiib7XAvFQiO25yZkIoOYjOTLKPeUIxB2u3A4HraJj51hYl1wU4jJKC3Dtz17Gw1DcPXLcMfpcMWqK1KmPudCg19tBJyKSd0Y4ug1NDGpiqrzSbrGr5g0VjTSUN7ArkalBkFSMXEJF/Or5+NxK/XzaHUyy+Rvh/6GK+EI/KufWH8JqDZkPZOr1686gUpdyjHtwmS28aV7TJxR0cUoRSyqXYRLuNhXn2Bpn6ot6tHYGsFo0A510+iqSO4Suoe7qfXX0jPckyQmlVZATlopxxlHr5WO0+efzuo5q3nXm18hVAYf3XBLQX+bv8yP1+2lzx+h3uquGI4Np5RCJnuysPPYMrpyHItWtlJOMEcpJx80lDew07FQrj8GbgkbrdJwVQQag0liEoqFONB3gHd1qx0VZE991bhlwy2877T3AYxYey8GnLktx6vUZ2M0U2ihsKfl5qmYQJKYBMIBnjz4JOcfVHkQ0gUXLMmPmNjKQjPIebCvAb5UgFoC2Yc2CmvnoEs52YyvGjW+Gvr8yUmue3r2MBAewBdTZuyYO7sqe/r803n6pqezPmayTPU4H3xO3ba1fWtOFW4gPEBCJmgYVmWECk+FbaTNBpdwUeGpIOgJ2vHpwWiQGl8Nh/sPs86hmCyscZRysrQMR+NRPG4PbYE27t9xPx/fBA+ugs4q+PCZH855DE40VjQy4FOfb09MtdCPZbKwRo2vhqBXzZDSHTljbRV2Qg3ze4brtqvvFwfgsWWq3V9P+m2pauFYVYedZfLkoSdZGFBrfcgz8cZXcM7k6poS4WpgFBMgt8ckHAsTTUTtC2uZqwyfO/cHOF943V4W1CxI6czR3TUag5FBO9hNIz2WXu/URlJMdCpiOjEpc5Xx8Dse5qMXfYpvXH5bwTtxIURSkneYGJ3ImCw8Ca3CkNv8aismFkHRsfSjlXJGQ/rFSqslCPVvm9WiqonJ3p69SKQdrraodtGosdJul3vCSQkkPSYw9tTX0ZBx3hSgmGxt38rh/sN2Gcdf5ueM+Wfk9bxrm9fSUN7A5y6Aj79eKZeFqISQnDDsHNqow9V0KWdRTW7F5PSW0/nrYjjriMpTuffle+05OdkG+OWLtc1realJdXmVxUc2wBaS+qpR6a2024VBKbqReIT2wbRwNcd8LWfL8NmHIRQNceVdVzIYGeS7G78LsTi3Pq+UqzVNa1J8MyNBTxh2fubGMllYwxkJsLVZfQayeYQKxarGVVk9Jk5FbX71fNtjAkpJncyOHA0d5DgVwtXAEBMgNzGx5+RYHpMaX03ReruX1S8bMcskGA2mdOSUucoyiImzVbhQxQTUzu4LF3+BD531IZvBFwI9L0d3V6T7TNJLOZOpmITLVJdCtqmjVd4qylxleZlf84HT/CoScO1LipjoRUVL7Ns6tpGQCXZ2JztydjZmj6IvFdIVk4nYOdX6axmwWk9dicIUk+0davt5/kEVNHb2grNH3O07Ue4p5/tXfJ/uExdTtepk7r/m/oLJXkN5AyEPxIU6b3Qpp3YYXFJ9zkZSTK496Vr6/crE+qZXVDpw93B3SiTBWFTZtc1rGfaqksrK7tQJyukYEzHxVNrtwqDWp6MDR1V4nhUq11zVjNftTfm9sxeczd0nwdI++P6D8NjOh7ngJxdwx6Y7uHKnIjSb5iu1JN+1NV3xhLFNFtZwnmNbLeNrMdb5lY0rOVKtztvqkCPDxHF+tFS12B4TjVIQk7Nbz+aR5Yqw+8v8o44kmWgYYoLyVwiETUxCsRCxRCxlsvBAEebkOLGsbpk9yA8yfSbBSDBlJ7+gZoGdYwI5iImlmATCAUIxxRZ0XHM2YjJeZMujcEIrKFoxmSyPic/tA6GSfL1xh2JiLVraAGubXx0EcKweE52Lcsk+RXC3z1UhUfX+erXYtSvCe6DvgMowkaO3CpcC1d5qwlbS7UQqJtKVzPMoRDEBmGMNNHxxXv7+Eo23nPgWDnz0ANs+sE11sxSIbIF6h/oPJTtyRPaOHI3XLH0NTRVN3H2SIrCBcEANEhynYuLMaTn1+MiKiY4QKFQx0e3CoNantoDKMNED/JxlHI1vXf4tqluXcMG71cX3wV/BrgOb6Brq4kOWz6fOX8cNa2/I+2/VQYROA6wzp6lQnDJX+Uk+fBk8u6DwcyoXVjauRLqUwf3ELqWKHK5JVdTmV8+nvVL5pdyWX1kTE5/bN66pwYXgs6/5LBetvZLEaev42Zt+ltc5MZEwxAR1odKmtGpr8RuMDKZMFu4v8oV1af1Sjlepi3Z5JHcpRy9WS+qW0GNdSEVCmV91hkl1RJESrZiAcnhDUjEZa1zzSMhXMSmFxwSSc3yqIkqxcX7Y6v3JQX469RXGWMpxXKz+8XmllrhcLq5ec3XW8Kud3TtpGVDPGSifWopJU2UTCPjbwtwXm/EifZBf11AXsUTMJiZu4cbjUm9INmLy6oPw94Uq/O38xecX/fhGQjZicrDvoD28D0Y2v5a5ynjbmrfxf6tUsGFjMBlJYPvYxrABOrHpRNzCzRbrXDvQdyBn6OF4FBOnaTc99TVb19qy+mU8fdPTrF5yOlder+73lx/Da/coQ+z9J8J717+3oA2BPQZC5xDFwJNQm7ixeEw2zN/Av577rzyzoZmLVl/Kx8/5eMGPkQ3OYX4XHkiOlEhRTKpV+mtPedJ3tNzq1ltWv2xSuhhBJTQ/cN0DbH7/Zq4+6epJec6RYIiJhWpfdaZbPuxQTHzFMb5qNFc2I13YbabpU2nTSzmLaxcTc6vjqAtZiomVYaJ3aloxAVXOkVLSO5zqMSmmz6POX5efx0SXcibRYwKKmDQH1WuWcKUuWs7uCp36CmM3v4JaXK7YBXefpHImmquaWdu8lu1z4aROVbbY2r5VdeSMMryvVLhy1ZU0lDfwmvdAuNJb0E42X9hJpta5o6O4nYMUtZSejZhof4nH5eHsBWcX/fhGQlbFJHDIHt4HI5dyQJVzhrzw8HJ4i+oOHbdi4i/zs2rOKrY2wzorQG7TsU1Z75tBTPwFKCZWKaetvy2FmLTV5g7+m1c1jz+/+8+8btVl3HwF/OZEePgX8J0zIFHmyqtF2In0wZl2uJoY28ZLCMH/XPI/HP/n4zz0joeYUzGn4MfIBm1o39WolFRNXJ2KWnqWCWDH0U9WGWcqYlzERAhxtRDiJSFEQgixIe1nnxJC7BFC7BRCvN5x+6XWbXuEEJ8cz/MXE+n5AnYbH9jtwsUs5eiLpC4n6CnAGumlHL0Ls0PWhrtSWoUhVTFpD7YTjAaJy7hNTPxl/nGlGaaj1lc7smISCuCNqdp7qKw0isn8gexqUX15fdL8WoRSDqiF8sV5sHsOXHfSdYCSiQf8KhvghB5LMenaaftLIHeGSSkwr2oeW27Zws/e9DO23LIla6DceJHeaq7HvWeb8JyNmJx/EP6yBM5oPWNMRHI8SCcmBwMH6Q312hsEj8szavnrvEXnMb96PnedjN2xMV6PCaid/9ML4ZzDqizwpwN/ynq/nuEekMkZUvkoJvX+eo5VK3Ptii645Xe38PDeh6kJKY93v29kda3KW8WD1z/Ie097L/91AVzyLlXGecuJb2FJ3ZKC/s70wZnZ4hCmAso95SyqXcTOOUrlO5hFUWupUmZh7TMRCeU73GuIybiwHXgL8KTzRiHEGuA64CTgUuDbQgi3EMIN3A5cBqwBrrfuW3JkyxdwlnIGvMUt5aR3hui6r8ZgZFCFGTlKOZDMMtFdOSnEJE0xyZX6WizU+etG9piEHXH0YnJzTEARk5aB7ItWumIyLvOrVfPuqFRlHI/Lw5tPfDNAxlj6vx76K93D3XaGic/tm5ByyXiwoGYB7zz1nXbWTbGRPplaT1XNRkzKy8pxC7dNTOqGldT9QkvxvACFIJ2YHAocArBLOQtrF44qv7tdbq5eczUPLYf1x2HeQKpiMtYN0MVLL6arUq0HZxyFx/c/nvV+PcM9VESVJyrsyY+YXL3mavY1wCdeC4/9DOqPB3hi/xPJcDUx+qiEMlcZd1xxB7dffjsdZ53ExWuv4ntv/F7Bf6dOd9XvgVMRLuVE3GxQLcPgj2cv9aUoJgPQam2khryGmIwZUsodUsqdWX50FXCXlDIspdwP7AHOtP7tkVLuk1JGgLus+5Yc6cRkIDyQWcqZTMUkGlTtwo5SDiQVkwN9B+ge7s6umEilmNgD/MbhWB8Jtb5agl6VTlsWz1RM+sP9tr8ESlPKaRnMrpg0+Bsykl/LXGUZXQX5YE3TGpbULeFDl6ld4A1rb7AX+5PmnoRA2MREe39WWhkmKxpXTEob8FRCimLiGGeQjZgIIVIiw887BM+2qlp9KYhJehlBQ5dy8m0zve7k6wh7VJrv214mxWMy1twYPT/n8aVw8T547shz9hrmRKEDEAGuPflaPnPBZ/jxafClc+Hxn0JrALsjB/Kb4SSE4B/P+Ee2/+N2fnvdb8dkstTmdV0GT5mFNYUUE1CjJnZbf+LBOrUGORUx3ZZ7rEopJqXoyJmKmCiPSSvQ5vj+sHVbrtszIIS4WQixUQixsbOzc4IOMwnb/JpNMQkX3/w6kmIipRyxlNM4nExRXBxIEpNhr+pEqQ1NnmKCwE7xTPeYlGKyMORWTFLMr+X1BKxAvZqwuiCOxfgKagf8+7f/njee9x7++cJ/41uXf8v+WZW3ihMaTkgxwMLU7MiZLKTMWQonb89GTCB1loku47iFm1ctfNUkHrVCeVk5Prcvg5joUs5Ixlcnzmo9i8W1i7n7ZNQUaqdiMsZSTmtNK6saV/H4Mrhov5pVpeP7nRgLMQH49wv+nU+86hPcfpbyhzz+M9hw1BGuNkkdJJCqeDpLOcVe48aLVXNW0VsBnRVKMUn3H3ndXpoqmmyPiZOYjBS6ONMxKjERQjwmhNie5d+EKh1SyjuklBuklBuamiZuaJlGtTfT/Lq9cztVYRXUNVjsUo5DMWlIU0xCsRASaZdyfG6fzaydWSZAimICjiyTYLv9mBNFTNIl+b5wX8rPSzFZGDIVEzt2O62UI13q2OYPKGVqPH6FNU1r+NFVP+LzF38+43HSO3M8MbXD3lc/tTpyJgvpiomGNiGPREwuOKDyS05rOW1SBkKmQ+/WncTEG1ObhWPV+SsmQgiuPelaHl2mWknXdCpV1i3c4wpxvHjpxTy5WJVy/NHs5Zye4Z4UlSFfYqJNoh8844N85Vz45SnwuSeScfQTPQXXicbyxkzzK1OvlKNbke84HTa1ZP+8t1Qns0w0MfG4PJNK9KYaRiUmUspLpJQnZ/n3wAi/dgRwvqoLrNty3V5yVHmr7Eh6UK7zu7ffzTu2wu9Xqq6OsxacVbTnq/HVIBBKMRlWpZtoXFnenUO9gh51bNXeajwuT0qWCShicrAuuVNzpr9OimKCpZiEsysmJS/l5DK/OhSrhf3qgjgW42s+WDt3LXsaFGGsCquwqcM1aibFbFRM/GV+PC6Pfd5ojKaYtPar7qZnWye/TdiJdGKyoF95BBKu0TtynLj25GuJlsFvVsNbX7ayknzV4wr3unjZxQxaQWHnHspNTMaimIAiJ9+47BvctP4mPnsB/OtrVcz6svplYyqDjhUN5Q1T3vwKalzCRUsv4v9dDMGmWj569kcz7mOnvw6oFurdjSpOotApyTMJE1XKeRC4TgjhE0IsBVYAzwHPAyuEEEuFEF6UQfbBCTqGgpDuMfneC99jODrMLRvV5MuFNQt5/QmvH/lBCoBLuKjz1ymfg7Vr1OWcYFS11uhSTqW3EiEEcyrmpCgm5VYZor1SScOQmv5qe0zGET40Epw732wThvvD/SUv5cy3Sjk+ty8l9t1pYlzQn/2CWCysbV5LwgUvN6nJts7hfbNRMRFCqHA+f6ZiMhIx2XBUmV7DntL4SzTSiYlzamy+pRyA9fPWs6JhBXedDBWx3AP8CsGFSy5EIJTPZL/qAtO+Jo3xEBNQa9f33vg93r/h/XzlXHh6iZv/7/z/b1zHXShSSjnW+lbhqZhUcpQPXMLFo+98lBff/yJ7Prwna3u7mpeTqpjMZn8JjL9d+M1CiMPAOcDvhRCPAEgpXwLuAV4GHgZulVLGpZQx4IPAI8AO4B7rviVHlbdKqRMRQKqI+LMPq+8fWwY3n35z0U2KDeUNtmICyXJOMGIRE6uNVXsfGisalcfEIia6E0C6sCekZigm0lIzxjhHYiSkKCahLF05aaWcUppf03dSejHuLVevV3AcHpPRkN6Zo42vMDsVE8gc5AejExMXyl8iEJy36LxJPV4nMohJIHtGxWgQQnDdydfx5yXQUVEcg31DeQPrW9bz+DJlgAX40/5k27CUMnOy8BhUBrfLzXff+F32fngvBz96kHeve/e4jrtQNJY3Js2vE2TuLxZcwsWp807NmY8yv3o+7VVqw7m8B/ZO0lThqYzxduX8Rkq5QErpk1I2Sylf7/jZ56WUJ0gpV0kpH3Lc/gcp5UrrZ58fz/MXE1XeKuJuZR7Vw98+8Dx8dwO4y8p472nvLfpz1pfXZ1VMdClHTxfWu6h0xcTpL9kwfwMCYSsmPcM9dAQ71Jhyt5paOuEeE4diIqXMUExK4TGpjlg+nrRdoV6Me8rVh2DIM3GlnKX1S6n0VNrERIerNZY32l0esw1jUUxABautbV5bUsk+nZg4w9UK9QVcf/L1xN3wj2+AZxaoLq3x4uKlF/PMAljdpQYFOss5w7FhwvGwTUw8Ls+4CPmy+mW01mTtX5hQNJQ3EPSCJw7zBq0BflOsjJMvWqpaiLnVOjXggwG/UUxM8qsFvVPRsfQNQ3DlTvjxenjz6jdPyMyQen99dsXEKuVURVK9D3Mq5tg5JpBKTJY3LGdOxZyULJNdPbtyDvArBpyKSV1aV44Od9MeE3+Zf9JkVicxAbUAp++mnKUcyG66LBZcwsUpzaekKiaztCNHoxDFRN93wAtPLyxtGQeyl3IO1ao050IDDE9sOpH/es1/8bu1PsTChXzmgs+M+/guXnoxkTL1Wl14IJWYZIujL9Zg0slEY0WjPWF4WW/qLKzpBmeWid2RUwSCOp1hiIkFrUro9Nf3bIYHV0FPBXxgwwcm5DlzKSa5SjlzyrMrJh6Xh5aqFpqrmlPSX3d27ZxQYqLJnL7ADEQGiCWU3JQRRz9J/hLIJCbZSjlO8ytMbCkHlAF221xLMbE8JlMp8XWykT7OAKmIyXBZJjF5/fLXM+yFhR9TwVMTEZNfCJy7dV8Ue4BfIcZXJz59/qfp/1Q/hz52iPUt68d9fOctOg+Py2P7TPb17rNncY1lTs5UhDP9dWmvUhumWqtwvmipttJfq0yGiYYhJhY0MRn0KkPpLRtVr/7qOau5cMmFE/KcoykmupTjVEx6ypU64Uokicmi2kW4XW6aK5tTFJNDgUMT2uPvdrmp8dWkxNJrQlKqycKQhZhkUUw8bg9V3ipbMZlI8yuo8kN3JXZWzpEaFb40W5E+mdoTh7hLDeZLfx8uWXYJ9159L9ed935+//bfc0brGSU44iQayhvs3Xp9SHlMnJ1xY0Ex1cRKbyXnLDyHJ5YmfSaP71OqyUwjJj3l4E1k33xMF6QrJm7hLsirNBNhiIkFJzF50yvq/2cWwC2n3zJhUme936GYyEyPiS7lVHnUsTVWNBJ3q9JIXShJTHRcfbpiIpGpcc0T8MGt9dVmHeTnnCw8mQP8AHxlypCQophkkXm1JA9WyWwCFZNTmlWewba5VkeOMKWcgIPQjjYW4G1r3sZ33/hdLl9x+SQeZXY4L4pzhmBhQKWfTqWLycVLL2Zzi/JftPQnyzkzhZjoMRDd1ud3KptfR0NrdSuLaxfz+fPhe6fDqxe/Go/bU+rDKikMMbHgJCYffE6pJeWecm5cd+OEPWd9eT2RMoi6lDqSsyvHoZgAdpZJBjFxKiZSPcdElnL0Y2Yb5Ocs5fT7JreU4xIuvG4voTJIoJ4/GynTxBAm1vwKyaClrc1Tc3jfZKPWV8uAVxESV2L884omE84ywuoudX4Ne6ceMUm44M9LVArsE/ufsDtyYPoTEyc5jAtVgp+uxMTtcnP32+5m6frXcMb6y8c0P2imYfYmuKRBp0gOesEbhztPUY75iaxb2j6H8tRY+owcE08qMemqUHVtnWHiJCb26PQIDPomnpikS/JaKUkv5cybRMUEVDknVBahz6/aqbMtwFoxiQnVjTWRF8T68npOnnsyP16/XWUv+OtndeR0rb8W6UqWTqcjMekph/XHkh054ynlFBtntp5JlbeKx5cNcvF+uPPUdv7jz//BvS/fC8wsYqI/49O1lAMqvPOJG58o9WFMGRjFxIJtfvXBz0+FoA8+cMbEmF41nC2r9cOppRxPTI0Tj7hT24VBEZPTjiUzTJylHETqlGFnXPNEqBa5FBNNULT5dTI9JqCJiSOrIctuqr5ceXyCXkBMbCkH4JuXfZPgCQvZuaqR2y+/3S45zUakx9JPW2Jy3JFhMkbz60TA4/Zw/uLz7YF+SPjck5/Dv+0Vvv07VeYMeqGpYuLHfUwEqrxVdhL2VJ0sbDB2GMXEwuLaxSysWcjnX91GT7lytm+Yv2FCnzN9kJ+WWYORoF3GQSRLDLqu2lWhUjB1q7BTMYFk+uveRkUYDtdYH+QJqFvW+et4OZvHJJT0mEx2KQeSxGSkqOp5lfP4U7XyfeS6TzFx4ZILOfSxQxP6HNMF2nOkY+nLpykxuXQP/OpkdftUKuWAKuf8YdcfcEv41F/hza/A3CD84DQ49QOKvFyx6opSH+aYkJxZ1D5lJwsbjB1GMbHgdrn55Vt/SeuGC7lgw1u45233TPhzOgf51Q+nduU4Jwunl3K6y3MQE2vQn1Mxmag5ORq1vtqcHhNXQvlkBrwlJCYj7KauP+V6+ivdvPom9fpMBWPlbIGtmPinn2JS7a3GLdz0lKtk4UO1ivhPtXbVS5ZdAgJ+diqceQT+/TWw7CPwhQtdnLbhjTz1D09x8tyTS32YY0ZjhUp/naqThQ3GDqOYOHDeovP4041/Gv2ORUK6YuIs5ejJwpBUTKq8VXjdXroqIiztS80wgUzFBCaemNT56+zJr0iHxyQcoDqs/gbpmtyuHIAFNQvY2ryL+09U32vy5sR5i85j480bef7I87x++euZWzl3Uo9xNsNODbb8SZLpQ0ySu/VOQHlMFtcunnJBZafMPYXLll/Gv6GCt1urW/l/62/iptNumlJ+mLHinAXncNfyl9k5R50zevSDwfSHISYlxEiKiZ4sDEmPSXKQ31EgNcMEsC+sk62YxNyqZl0VSfWYlCKOXuOfz/lnrj78LN+bG+QDGz6QMzZ73bx1rJu3blKPzSBTMYm4pw8xAVKJSe3UMr5qCCF48PoHeXjPw1R5qzhv0XkzamLtf130X/SH+2nrb+Ou8/5t0tcYg4nDzDlLpyFqfDUIBL1+SX1IEZJoPKo8JllKOaB8Jk5i4lQCPG4PDeUNtFf2cJJaM+2AtQUTqJhA8gKjvSX94X7bXwKTX8q5bMVlHPzoQQYiA1nVEoPSIl0xCXqmIzFRXx+qhbOmmL9Eo8xVxhtXvrHUhzEhmFc1j3uunviSu8Hkw3hMSgiXcFHnr1ND5nT6a6hXeUyylHIgOcgPMokJkJH+qhWTiXKsO02MdSHoC/cBpZss7ERjRaMhJVMU6YR2OnlMIElMgh6VZzKVOnIMDKY7DDEpMXTLqjOWfjAyqBSTtFIOWIP8KiDkTs0w0UhPf50Mjwkkd77O5NdSlnIMpjb0UEd93kw3YrKodhH76uHH6wABqxpnb1iegUGxYYhJiZESS4+lmESCdhw9pJZyTpxzIvvq4ZOXKFPpqc2npjyeUzERCTUpud83sR4TcCgm2mMSCthx9M77GRhoOMcZOIlJeVl5aQ8sD9x8+s2I+no+9AblU3rDyjeU+pAMDGYMjMekxMimmOhSjlZMnKWc9294Pw/sfIBvlG3hTavflNHi2lyZVExqrK6YhGsSFBPrArMrnPSY6Dh6KE0px2BqQ6UGd9qqXm85+Nw+28w9lbFu3jp2fnAn+/v2s37e+lk/28TAoJgwxKTEqPfXczhNMdGlnMEsisn86vlsev8mhqPDVHgqMloUm6uaCfhVrP78gYmNo4csHpMcXTlGMTFIh62YWKWcIzXTo4yj0VTZRFPl9ExONTCYyjDEpMSo96cqJt1D3YRiIbuUIxCUe1KlbZdw5Rw411xpxdJXwqruiY9rzuYxicQjhGIh2/zqFu5pdcExmBzYc5YcpRxznhgYGIzLYyKE+LIQ4hUhxFYhxG+EEHWOn31KCLFHCLFTCPF6x+2XWrftEUJ8cjzPPxPQUN6Q9JhIODJwBEhOFq7wVOAS+b9NzvTXVV0Tr5hoE6NWTKKJKNfedy2gUjH7fVZb9BQLnzIoPdIVE0NMDAwMYPzm10eBk6WUa4FdwKcAhBBrgOuAk4BLgW8LIdxCCDdwO3AZsAa43rrvrEV9eT2RMoi61DThtv42ALuUk0sZyQVn+qtTMZnIuOY6fx0BRyz9/730W778CFx4AP6wAlY0zt4puga5UetX4wyMYmJgYODEuEo5Uso/Or59Bnib9fVVwF1SyjCwXwixBzjT+tkeKeU+ACHEXdZ9Xx7PcUxn2LH0lmpyuP8wYCkm3tRW4XzgVExO7ISdarzOhBITNS+ng9oQNA3C3fdB2A0bboZEQx13XvqNCXtug+mLWl9tRruwISYGBgbFbBf+B7CGMkAr0Ob42WHrtly3Z0AIcbMQYqMQYmNnZ2cRD3NqwY6lt3wmmpjoSHqn8TUf2LH0lbB6Eko5+rEDPlh3HDbeAU8tgje8AxYsXcvG923k7AVnT9hzG0xf1PpqGfQqUlIdMcTEwMBAYVTFRAjxGDAvy48+LaV8wLrPp4EYcGexDkxKeQdwB8CGDRtksR53qiFdMdmpFZMxlnL8ZX5qfbW0VwVosNowBWJC23Ubyhs4Wq08Je96Mzy4Gt5xyju444o7zIXGICdq/bVIl5o+PW9QEZNGc74YGMx6jEpMpJSXjPRzIcS7gTcCF0spNYE4Aix03G2BdRsj3D4rka6YROIRIFnKKVQxAZ3+qvJE+vzKfFqIgbZQXL7icj6y9xHm/gskvGXc9rqv8sEzP2gMrwYjwjnIr2XAKCYGBgYK4/KYCCEuBT4BXCClHHL86EHgl0KIrwLzgRXAc4AAVgghlqIIyXXA28dzDNMd6YqJhi7lNBXoMQGd/rpLPe4ExtFrfOjMD1HlrWJH5w5uWHsDp847dfRfMpj1cLaaLw4YYmJgYKAw3hyTbwE+4FFrd/yMlPIWKeVLQoh7UKbWGHCrlDIOIIT4IPAI4AZ+JKV8aZzHMK2hFZOe8mSWCWBPFy60lANKMXnJ+rWJnJOjIYTgH9b/w4Q+h8HMgz1h2PJBGWJiYGAA4+/KWT7Czz4PfD7L7X8A/jCe551JqPHVIBD0+mWKYqKnC4+plFPZzBOW0NLnT5IfA4OpBLuUY6UDG2JiYGAAZohfyeESLur8daqUk66YeApvFwZFTHr9KhtlMhQTA4OxIF0xCZUZYmJgYGCIyZSAPchPKyZyfObX1ppWpAu2NMOxaphTPqe4B2xgUAQ4FZOgBxCGmBgYGJhZOVMC9f56esuhwVJM/DGIuNVU4LF4TK5YeQVV3irOeP8gAsG1J19b5CM2MBg/nIrJkDWc1xATAwMDQ0ymAGzFxCImuowDY1NMmiqb2HrLVh7c+SAb5m/g3EXnFvFoDQyKAz1nKeCLGGJiYGBgwxCTKYB6fz2HHe3CerIwjM1jArC0fikfOfsjRTpCA4OJgRpn0GmIiYGBgQ3jMZkCqPenKSZRh2IyhlKOgcF0Qa2/1pRyDAwMUmCIyRRAfXl9MmBNJuPoYWylHAOD6QI9yM8QEwMDAw1DTKYA6v31RMpUe29lJNmRA2Mv5RgYTAesbV7L0wvhv89TM51Wz1ld6kMyMDAoMYzHZArAnpdjqSZVEVPKMZgd+PSrP832ju0827CXL577SRbULCj1IRkYGJQYhphMAdjzciyfiSnlGMwWnNBwAs+977lSH4aBgcEUginlTAE0lDcAScXEWcoxiomBgYGBwWyCISZTAHYpx1JMnKUc4zExMDAwMJhNMMRkCsAu5WjFxJRyDAwMDAxmKQwxmQJIV0x0Kcct3Hjd3hIfnYGBgYGBweTBEJMpgBpfDQKRopjoycJCiFIfnoGBgYGBwaTBEJMpAJdwUeevS/WYeI3x1cDAwMBg9sEQkymC+vJ6ehxdOYNe4y8xMDAwMJh9GBcxEUJ8TgixVQjxohDij0KI+dbtQghxmxBij/Xz0xy/c6MQYrf178bx/gEzBfV+K5Z+OFnKMYqJgYGBgcFsw3gVky9LKddKKdcBvwP+3br9MmCF9e9m4DsAQogG4D+As4Azgf8QQtSP8xhmBOrLrUF+oWQpx7QKGxgYGBjMNoyLmEgp+x3fVgLS+voq4GdS4RmgTgjRArweeFRK2SOl7AUeBS4dzzHMFGjFpGHYlHIMDAwMDGYvxh1JL4T4PPAuIAC8xrq5FWhz3O2wdVuu22c96v31tvk16lKlnAWmlGNgYGBgMMswqmIihHhMCLE9y7+rAKSUn5ZSLgTuBD5YrAMTQtwshNgohNjY2dlZrIedsqgvr08d4mdKOQYGBgYGsxCjKiZSykvyfKw7gT+gPCRHgIWOny2wbjsCXJh2+59zPO8dwB0AGzZskNnuM5NQ768nUqbUkrlBU8oxMDAwMJidGG9XzgrHt1cBr1hfPwi8y+rOORsISCmPAY8ArxNC1Fum19dZt8162Omv5VARs7pyDDExMDAwMJhlGK/H5H+EEKuABHAQuMW6/Q/A5cAeYAh4D4CUskcI8Tngeet+n5VS9ozzGGYE7Hk5fmgZgGHTLmxgYGBgMAsxLmIipXxrjtslcGuOn/0I+NF4nncmwqmYDHkAYTwmBgYGBgazDyb5dYrAqZiYycIGBgYGBrMVhphMETgVk6AmJqaUY2BgYGAwy2CIyRSBUzEJetRtppRjYGBgYDDbYIjJFEGtvxaBoLfclHIMDAwMDGYvDDGZInAJF3X+OqWYmFKOgYGBgcEshSEmUwj15fX0lCdLOUYxMTAwMDCYbRj3rByD4uHM1jP5/cp9bGtW/pJVc1aV+pAMDAwMDAwmFYaYTCH898X/TV+oj+ODx/nFBZ+hwlNR6kMyMDAwMDCYVBhiMoWwpG4JD73joVIfhoGBgYGBQclgPCYGBgYGBgYGUwaGmBgYGBgYGBhMGRhiYmBgYGBgYDBlYIiJgYGBgYGBwZSBISYGBgYGBgYGUwaGmBgYGBgYGBhMGRhiYmBgYGBgYDBlIKSUpT6GUSGE6AQOTtDDzwG6JuixDbLDvOaTC/N6Ty7M6z25MK/35KKYr/diKWVT+o3TgphMJIQQG6WUG0p9HLMJ5jWfXJjXe3JhXu/JhXm9JxeT8XqbUo6BgYGBgYHBlIEhJgYGBgYGBgZTBoaYwB2lPoBZCPOaTy7M6z25MK/35MK83pOLCX+9Z73HxMDAwMDAwGDqwCgmBgYGBgYGBlMGhpgYGBgYGBgYTBnMamIihLhUCLFTCLFHCPHJUh/PTIMQYqEQ4k9CiJeFEC8JIT5i3d4ghHhUCLHb+r++1Mc6kyCEcAshNgshfmd9v1QI8ax1nt8thPCW+hhnCoQQdUKI+4QQrwghdgghzjHn98RCCPExaz3ZLoT4lRDCb87x4kEI8SMhRIcQYrvjtqzntFC4zXrdtwohTivGMcxaYiKEcAO3A5cBa4DrhRBrSntUMw4x4J+klGuAs4Fbrdf4k8DjUsoVwOPW9wbFw0eAHY7vvwh8TUq5HOgFbirJUc1MfAN4WEq5GjgV9bqb83uCIIRoBT4MbJBSngy4gesw53gx8RPg0rTbcp3TlwErrH83A98pxgHMWmICnAnskVLuk1JGgLuAq0p8TDMKUspjUspN1tcDqEW7FfU6/9S620+BN5XkAGcghBALgDcAP7C+F8BFwH3WXczrXSQIIWqB84EfAkgpI1LKPsz5PdEoA8qFEGVABXAMc44XDVLKJ4GetJtzndNXAT+TCs8AdUKIlvEew2wmJq1Am+P7w9ZtBhMAIcQSYD3wLNAspTxm/eg40Fyq45qB+DrwCSBhfd8I9EkpY9b35jwvHpYCncCPrdLZD4QQlZjze8IgpTwCfAU4hCIkAeAFzDk+0ch1Tk/IdXQ2ExODSYIQogr4NfBRKWW/82dS9aubnvUiQAjxRqBDSvlCqY9llqAMOA34jpRyPRAkrWxjzu/iwvI2XIUihfOBSjLLDgYTiMk4p2czMTkCLHR8v8C6zaCIEEJ4UKTkTinl/dbN7Vrus/7vKNXxzTCcC1wphDiAKk1ehPJA1FmyN5jzvJg4DByWUj5rfX8fiqiY83vicAmwX0rZKaWMAvejzntzjk8scp3TE3Idnc3E5HlgheXm9qIMVA+W+JhmFCx/ww+BHVLKrzp+9CBwo/X1jcADk31sMxFSyk9JKRdIKZegzucnpJTvAP4EvM26m3m9iwQp5XGgTQixyrrpYuBlzPk9kTgEnC2EqLDWF/2am3N8YpHrnH4QeJfVnXM2EHCUfMaMWZ38KoS4HFWTdwM/klJ+vrRHNLMghDgP+CuwjaTn4d9QPpN7gEXAQeAaKWW62cpgHBBCXAj8s5TyjUKIZSgFpQHYDNwgpQyX8PBmDIQQ61BGYy+wD3gPasNnzu8JghDiP4FrUV1/m4H3onwN5hwvAoQQvwIuBOYA7cB/AL8lyzltkcNvocppQ8B7pJQbx30Ms5mYGBgYGBgYGEwtzOZSjoGBgYGBgcEUgyEmBgYGBgYGBlMGhpgYGBgYGBgYTBkYYmJgYGBgYGAwZWCIiYGBgYGBgcGUgSEmBgYGBgYGBlMGhpgYGBgYGBgYTBn8/3u55GHxAgQfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_predict = predict(X, theta)\n",
    "plt.figure(figsize=(9, 4))\n",
    "plt.plot(y, color='green', linewidth=4)\n",
    "plt.plot(y_predict, color='red', linewidth=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(X, y, theta, l_rate, iterations):\n",
    "    cost_history = [0] * iterations\n",
    "    for epoch in range(iterations):\n",
    "        for i, row in enumerate(X): #什么作用？\n",
    "            r = random.random()\n",
    "            if r >= 0.07:\n",
    "                continue\n",
    "            yhat = np.dot(row, theta)\n",
    "            loss = yhat[0] - y[i]\n",
    "            theta = theta - l_rate * loss * row.reshape((-1, 1)) # 为什么？\n",
    "        cost_history[epoch] += loss ** 2\n",
    "    return theta, cost_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.random.rand(X.shape[1], 1)\n",
    "iterations = 100\n",
    "l_rate = 0.01\n",
    "theta, cost_history = sgd(X, y, theta, l_rate, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[49.05333584, 74.16720217, 94.58759025]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 训练之后， 显示得到的参数\n",
    "theta.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[49.04322548, 74.20224438, 94.62227394]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 对照一下， 采用scikit-learn学习到的参数\n",
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x16054485048>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(range(iterations), cost_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([3866.52283542]),\n",
       " array([27.2165774]),\n",
       " array([2779.86309743]),\n",
       " array([14582.81794683]),\n",
       " array([410.108678]),\n",
       " array([976.71755167]),\n",
       " array([942.77353957]),\n",
       " array([2405.76997183]),\n",
       " array([8840.13793274]),\n",
       " array([930.41819489]),\n",
       " array([19.64128986]),\n",
       " array([0.37608396]),\n",
       " array([3063.51280571]),\n",
       " array([2551.86874051]),\n",
       " array([18.7805555]),\n",
       " array([1782.26885638]),\n",
       " array([0.08867506]),\n",
       " array([1510.8531652]),\n",
       " array([177.68922679]),\n",
       " array([1148.13064536]),\n",
       " array([777.18232997]),\n",
       " array([21.49023477]),\n",
       " array([507.97745053]),\n",
       " array([318.0180869]),\n",
       " array([544.08619914]),\n",
       " array([503.27498855]),\n",
       " array([448.66833522]),\n",
       " array([453.21076388]),\n",
       " array([18.22478763]),\n",
       " array([20.02599123]),\n",
       " array([273.50005066]),\n",
       " array([175.03104462]),\n",
       " array([217.69576617]),\n",
       " array([3.95666744]),\n",
       " array([173.84300116]),\n",
       " array([19.04006779]),\n",
       " array([329.2310532]),\n",
       " array([171.37781479]),\n",
       " array([0.34489144]),\n",
       " array([54.66836488]),\n",
       " array([8.11072153]),\n",
       " array([42.66465711]),\n",
       " array([0.00216511]),\n",
       " array([0.33571684]),\n",
       " array([2.00924828]),\n",
       " array([0.23234798]),\n",
       " array([1.47551699]),\n",
       " array([1.09329514]),\n",
       " array([14.70465885]),\n",
       " array([18.3660296]),\n",
       " array([0.00562437]),\n",
       " array([8.12208413]),\n",
       " array([1.02304403]),\n",
       " array([0.12309438]),\n",
       " array([0.03195363]),\n",
       " array([0.0740846]),\n",
       " array([9.02932379]),\n",
       " array([6.83242126]),\n",
       " array([0.27257537]),\n",
       " array([0.14973099]),\n",
       " array([16.59473044]),\n",
       " array([3.70941597]),\n",
       " array([0.04187043]),\n",
       " array([0.01253493]),\n",
       " array([3.65537676]),\n",
       " array([1.89051677]),\n",
       " array([0.01475029]),\n",
       " array([0.55104131]),\n",
       " array([0.02837636]),\n",
       " array([0.00448195]),\n",
       " array([0.29424979]),\n",
       " array([0.08460851]),\n",
       " array([0.02554308]),\n",
       " array([0.38032654]),\n",
       " array([0.11024783]),\n",
       " array([0.01478286]),\n",
       " array([0.0297545]),\n",
       " array([0.00208082]),\n",
       " array([0.00120911]),\n",
       " array([0.00148082]),\n",
       " array([0.01814327]),\n",
       " array([0.05758967]),\n",
       " array([0.00126043]),\n",
       " array([0.03737405]),\n",
       " array([0.0011785]),\n",
       " array([0.03494869]),\n",
       " array([0.08022058]),\n",
       " array([0.00161776]),\n",
       " array([0.01723076]),\n",
       " array([0.00487248]),\n",
       " array([0.00405041]),\n",
       " array([0.01886529]),\n",
       " array([0.00736093]),\n",
       " array([0.00596626]),\n",
       " array([0.00656944]),\n",
       " array([0.00201117]),\n",
       " array([0.0002597]),\n",
       " array([0.0051392]),\n",
       " array([1.83137362e-05]),\n",
       " array([1.46217714e-05])]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[49.14107964 73.63691474 94.13556988]]\n",
      "[[49.04322548 74.20224438 94.62227394]]\n"
     ]
    }
   ],
   "source": [
    "def sgd_batch_two(X, y, theta, l_rate, iterations, batch_size=2):\n",
    "    cost_history = [0] * iterations\n",
    "    for epoch in range(iterations):\n",
    "        i = random.randint(0, X.shape[0] - 1)\n",
    "        j = random.randint(0, X.shape[0] - 1)\n",
    "        row_i = X[i]\n",
    "        row_j = X[j]\n",
    "        yhat_i = np.dot(row_i, theta)\n",
    "        yhat_j = np.dot(row_j, theta)\n",
    "        loss_i = yhat_i[0] - y[i] \n",
    "        loss_j = yhat_j[0] - y[j] \n",
    "        loss = (loss_i + loss_j) / 2\n",
    "        theta = theta - l_rate * loss * (row_i + row_j).reshape((-1, 1)) / 2 \n",
    "        cost_history[epoch] += loss ** 2\n",
    "    return theta, cost_history\n",
    "theta = np.random.rand(X.shape[1], 1)\n",
    "iterations = 100\n",
    "l_rate = 0.1\n",
    "theta, cost_history = sgd_batch_two(X, y, theta, l_rate, iterations)\n",
    "print(theta.T)\n",
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x16054577c48>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(range(iterations), cost_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([24156.61175475]),\n",
       " array([333.41590645]),\n",
       " array([11.83902731]),\n",
       " array([7114.57813397]),\n",
       " array([813.83608733]),\n",
       " array([1729.98115933]),\n",
       " array([758.09482126]),\n",
       " array([30439.58597915]),\n",
       " array([183.10234816]),\n",
       " array([60.37286234]),\n",
       " array([556.12710584]),\n",
       " array([53.23786688]),\n",
       " array([4512.88406218]),\n",
       " array([3980.49109403]),\n",
       " array([0.00193558]),\n",
       " array([1557.48222343]),\n",
       " array([5303.42283735]),\n",
       " array([2373.83027779]),\n",
       " array([3262.56190491]),\n",
       " array([276.71722219]),\n",
       " array([19.78674408]),\n",
       " array([16.79642464]),\n",
       " array([341.80451321]),\n",
       " array([296.9571818]),\n",
       " array([623.319151]),\n",
       " array([251.30346558]),\n",
       " array([293.59901998]),\n",
       " array([837.32452229]),\n",
       " array([1065.99947051]),\n",
       " array([0.1527934]),\n",
       " array([436.58047648]),\n",
       " array([3.7462421]),\n",
       " array([139.19965469]),\n",
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